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cOin Toss Paradox

FillFueler
Posts: 18
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3/14/2016 9:15:03 AM
Posted: 8 months ago
I get eight heads in a row using an unbiased coin. Now, before I flip this coin one more time, tell me - is the probability for me to get a head (pun not intended) still 0.5?
Deb-8-A-Bull
Posts: 2,181
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3/14/2016 9:20:38 AM
Posted: 8 months ago
At 3/14/2016 9:15:03 AM, FillFueler wrote:
I get eight heads in a row using an unbiased coin. Now, before I flip this coin one more time, tell me - is the probability for me to get a head (pun not intended) still 0.5?

1st post
Of course it is.
Deb-8-A-Bull
Posts: 2,181
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3/14/2016 9:29:14 AM
Posted: 8 months ago
At 3/14/2016 9:20:38 AM, Deb-8-A-Bull wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
I get eight heads in a row using an unbiased coin. Now, before I flip this coin one more time, tell me - is the probability for me to get a head (pun not intended) still 0.5?

1st post
Of course it is.

You coin flipping technique can come into play, so it not the best way to look at it.
FillFueler
Posts: 18
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3/14/2016 9:31:16 AM
Posted: 8 months ago
At 3/14/2016 9:20:38 AM, Deb-8-A-Bull wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
I get eight heads in a row using an unbiased coin. Now, before I flip this coin one more time, tell me - is the probability for me to get a head (pun not intended) still 0.5?

1st post
Of course it is.

Practically it is not. Hence the paradox.
Deb-8-A-Bull
Posts: 2,181
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3/14/2016 9:33:45 AM
Posted: 8 months ago
At 3/14/2016 9:31:16 AM, FillFueler wrote:
At 3/14/2016 9:20:38 AM, Deb-8-A-Bull wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
I get eight heads in a row using an unbiased coin. Now, before I flip this coin one more time, tell me - is the probability for me to get a head (pun not intended) still 0.5?

1st post
Of course it is.

Practically it is not. Hence the paradox.

Don't be silly
RuvDraba
Posts: 6,033
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3/14/2016 9:34:32 AM
Posted: 8 months ago
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.
FillFueler
Posts: 18
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3/14/2016 2:12:36 PM
Posted: 8 months ago
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.
FillFueler
Posts: 18
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3/14/2016 2:25:32 PM
Posted: 8 months ago
#7 EDIT :-:

EXPERIMENT
Take an unbiased coin. First, get 3 tails and NOW note whether or not the probability of getting a head or tail is still half the fourth time. Anyone can do this. As long as I am getting more heads than tails the fourth time after observing 3 tails , there is a problem.

Note the observation you get fourth time. The only requirement for this experiment is the successful observation of head or tail 3 times in a row each time before flipping the coin fourth time.
TBR
Posts: 9,991
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3/14/2016 2:34:32 PM
Posted: 8 months ago
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics. PROBABILITY that you will get heads is always the same.
liltankjj
Posts: 430
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3/14/2016 2:47:57 PM
Posted: 8 months ago
You are talking probability vs statistics. PROBABILITY that you will get heads is always the same.

Best way to put it right there. +1
FillFueler
Posts: 18
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3/14/2016 3:30:44 PM
Posted: 8 months ago
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.
TBR
Posts: 9,991
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3/14/2016 3:35:18 PM
Posted: 8 months ago
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions. The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.
FillFueler
Posts: 18
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3/14/2016 3:46:03 PM
Posted: 8 months ago
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.
TBR
Posts: 9,991
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3/14/2016 4:01:47 PM
Posted: 8 months ago
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.
FillFueler
Posts: 18
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3/14/2016 4:18:50 PM
Posted: 8 months ago
At 3/14/2016 4:01:47 PM, TBR wrote:
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

TBR-
1. How can you say 'all were 50:50'?
2. In #8, is the 4th coin toss not an independent event?

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.
TBR
Posts: 9,991
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3/14/2016 4:32:32 PM
Posted: 8 months ago
At 3/14/2016 4:18:50 PM, FillFueler wrote:
At 3/14/2016 4:01:47 PM, TBR wrote:
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

TBR-
1. How can you say 'all were 50:50'?
2. In #8, is the 4th coin toss not an independent event?

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.

OK. Lets work this through. Lets say I am sitting with you flipping this coin. We are betting 1$ each flip, you win on heads, I win on tails. So far, you have one 10 times, I have one 0. How "odd" is this? What is the probability of getting this odd result?

(.5)^10 = .0009765625

That is fine, looking backwards, and calling you a lucky bastard. But, I am foolish, thinking this NEXT flip, I must be do. No. The next flip I am wondering, what are my chances of getting a buck back?

.5

---------------------------------------------------------------------------------------

So. If I were a betting man, and I am, I would take the bet that you can't get 10 head in a row, and feel very comfortable. I would be much less interested in the 1$ per flip bet.

This make sense?
Deb-8-A-Bull
Posts: 2,181
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3/14/2016 4:38:59 PM
Posted: 8 months ago
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics. PROBABILITY that you will get heads is always the same.

Could there be a argument for . If someone flipped a coin and you had to guess heads or tails . That's not 50/50.
Now here is the funny bit. There might be a speck of a chance , they could be a "professional" coin flipper, even if it's ya mum or ya best friend flipping the coin ,

I don't think you could not know ,if your mum or best mate were pro coin flippers. Rigging it for or against you . And if that could be a minute speck of a chance ,then when anyone flips a coin 100% TRULY. and you have to call .
That's not a true 50/50 because there might be a chance that they are a pro coin flipper .

Even magic could Change the odds . As in magicians crap . With all them Avenues as stupid as they are . No person in the world could flip a coin truly for you and it be. 50 / 50
50 .001 / 49.999.
FillFueler
Posts: 18
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3/14/2016 4:43:09 PM
Posted: 8 months ago
At 3/14/2016 4:32:32 PM, TBR wrote:
At 3/14/2016 4:18:50 PM, FillFueler wrote:
At 3/14/2016 4:01:47 PM, TBR wrote:
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

TBR-
1. How can you say 'all were 50:50'?
2. In #8, is the 4th coin toss not an independent event?

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.

OK. Lets work this through. Lets say I am sitting with you flipping this coin. We are betting 1$ each flip, you win on heads, I win on tails. So far, you have one 10 times, I have one 0. How "odd" is this? What is the probability of getting this odd result?

(.5)^10 = .0009765625

That is fine, looking backwards, and calling you a lucky bastard. But, I am foolish, thinking this NEXT flip, I must be do. No. The next flip I am wondering, what are my chances of getting a buck back?

.5

---------------------------------------------------------------------------------------

So. If I were a betting man, and I am, I would take the bet that you can't get 10 head in a row, and feel very comfortable. I would be much less interested in the 1$ per flip bet.

This make sense?

you do not have the answers for my two questions?
RuvDraba
Posts: 6,033
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3/14/2016 4:50:52 PM
Posted: 8 months ago
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.
You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.
Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.
Do you believe that the experiment I proposed is substantially different to the experiment you proposed?

For example, if I start with 32 coins, toss them, and begin creating piles reflecting the outcomes, then after three tosses per coin, we will likely have eight outcomes piles:
HHH HHT HTH HTT THH THT TTH TTT

Since there are eight ordered outcomes, all equally likely, we should have around four coins in each pile.

Now, let's keep only the HHH pile with its four or so coins. Toss them each again. That will repeat your HHH experiment approximately four times, yes?

What do you predict will happen to that pile?
TBR
Posts: 9,991
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3/14/2016 5:03:26 PM
Posted: 8 months ago
At 3/14/2016 4:43:09 PM, FillFueler wrote:
At 3/14/2016 4:32:32 PM, TBR wrote:
At 3/14/2016 4:18:50 PM, FillFueler wrote:
At 3/14/2016 4:01:47 PM, TBR wrote:
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

TBR-
1. How can you say 'all were 50:50'?
2. In #8, is the 4th coin toss not an independent event?

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.

OK. Lets work this through. Lets say I am sitting with you flipping this coin. We are betting 1$ each flip, you win on heads, I win on tails. So far, you have one 10 times, I have one 0. How "odd" is this? What is the probability of getting this odd result?

(.5)^10 = .0009765625

That is fine, looking backwards, and calling you a lucky bastard. But, I am foolish, thinking this NEXT flip, I must be do. No. The next flip I am wondering, what are my chances of getting a buck back?

.5

---------------------------------------------------------------------------------------

So. If I were a betting man, and I am, I would take the bet that you can't get 10 head in a row, and feel very comfortable. I would be much less interested in the 1$ per flip bet.

This make sense?

you do not have the answers for my two questions?

1. How can you say 'all were 50:50'?
You set the conditions. You said it was a "fair coin".

2. In #8, is the 4th coin toss not an independent event?
As I have said numerous times, each flip is an independent event, yes. Its possible I am not understanding your question here.

I think you are stuck on independent events and multiplication. P(A) P(B). Each independently has a .5 probability, but the problibity of intersection of the two is .25.

Flip one potential outcomes.
H T

Flip two potential outcomes.
H T

Flip 1 and 2 combined potential outcomes
(H T) (H T)
(.5)(.5)

OR put another way, I flip the coin twice this is what I can get
HH
HT
TT
TH

Out of that set, I see the .25 of getting exactly HH.
FillFueler
Posts: 18
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3/14/2016 5:13:39 PM
Posted: 8 months ago
At 3/14/2016 5:03:26 PM, TBR wrote:
At 3/14/2016 4:43:09 PM, FillFueler wrote:
At 3/14/2016 4:32:32 PM, TBR wrote:
At 3/14/2016 4:18:50 PM, FillFueler wrote:
At 3/14/2016 4:01:47 PM, TBR wrote:
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

TBR-
1. How can you say 'all were 50:50'?
2. In #8, is the 4th coin toss not an independent event?

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.

OK. Lets work this through. Lets say I am sitting with you flipping this coin. We are betting 1$ each flip, you win on heads, I win on tails. So far, you have one 10 times, I have one 0. How "odd" is this? What is the probability of getting this odd result?

(.5)^10 = .0009765625

That is fine, looking backwards, and calling you a lucky bastard. But, I am foolish, thinking this NEXT flip, I must be do. No. The next flip I am wondering, what are my chances of getting a buck back?

.5

---------------------------------------------------------------------------------------

So. If I were a betting man, and I am, I would take the bet that you can't get 10 head in a row, and feel very comfortable. I would be much less interested in the 1$ per flip bet.

This make sense?

you do not have the answers for my two questions?




1. How can you say 'all were 50:50'?
You set the conditions. You said it was a "fair coin".

2. In #8, is the 4th coin toss not an independent event?
As I have said numerous times, each flip is an independent event, yes. Its possible I am not understanding your question here.

I think you are stuck on independent events and multiplication. P(A) P(B). Each independently has a .5 probability, but the problibity of intersection of the two is .25.

Flip one potential outcomes.
H T

Flip two potential outcomes.
H T

Flip 1 and 2 combined potential outcomes
(H T) (H T)
(.5)(.5)

OR put another way, I flip the coin twice this is what I can get
HH
HT
TT
TH

Out of that set, I see the .25 of getting exactly HH.

#8. has that we already have HH / TT three times in a row (a requirement to carry out the experiment) . It doesn't matter if the probability is 0.25

I am interested in that 4th coin toss.
Deb-8-A-Bull
Posts: 2,181
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3/14/2016 5:18:27 PM
Posted: 8 months ago
At 3/14/2016 5:13:39 PM, FillFueler wrote:
At 3/14/2016 5:03:26 PM, TBR wrote:
At 3/14/2016 4:43:09 PM, FillFueler wrote:
At 3/14/2016 4:32:32 PM, TBR wrote:
At 3/14/2016 4:18:50 PM, FillFueler wrote:
At 3/14/2016 4:01:47 PM, TBR wrote:
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

TBR-
1. How can you say 'all were 50:50'?
2. In #8, is the 4th coin toss not an independent event?

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.

OK. Lets work this through. Lets say I am sitting with you flipping this coin. We are betting 1$ each flip, you win on heads, I win on tails. So far, you have one 10 times, I have one 0. How "odd" is this? What is the probability of getting this odd result?

(.5)^10 = .0009765625

That is fine, looking backwards, and calling you a lucky bastard. But, I am foolish, thinking this NEXT flip, I must be do. No. The next flip I am wondering, what are my chances of getting a buck back?

.5

---------------------------------------------------------------------------------------

So. If I were a betting man, and I am, I would take the bet that you can't get 10 head in a row, and feel very comfortable. I would be much less interested in the 1$ per flip bet.

This make sense?

you do not have the answers for my two questions?




1. How can you say 'all were 50:50'?
You set the conditions. You said it was a "fair coin".

2. In #8, is the 4th coin toss not an independent event?
As I have said numerous times, each flip is an independent event, yes. Its possible I am not understanding your question here.

I think you are stuck on independent events and multiplication. P(A) P(B). Each independently has a .5 probability, but the problibity of intersection of the two is .25.

Flip one potential outcomes.
H T

Flip two potential outcomes.
H T

Flip 1 and 2 combined potential outcomes
(H T) (H T)
(.5)(.5)

OR put another way, I flip the coin twice this is what I can get
HH
HT
TT
TH

Out of that set, I see the .25 of getting exactly HH.

#8. has that we already have HH / TT three times in a row (a requirement to carry out the experiment) . It doesn't matter if the probability is 0.25

I am interested in that 4th coin toss.

The 4th toss of a coin is the 1st toss
The 60774 flip of a coin is the 1st toss
50/50
TBR
Posts: 9,991
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3/14/2016 5:20:11 PM
Posted: 8 months ago
At 3/14/2016 5:13:39 PM, FillFueler wrote:
At 3/14/2016 5:03:26 PM, TBR wrote:
At 3/14/2016 4:43:09 PM, FillFueler wrote:
At 3/14/2016 4:32:32 PM, TBR wrote:
At 3/14/2016 4:18:50 PM, FillFueler wrote:
At 3/14/2016 4:01:47 PM, TBR wrote:
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

TBR-
1. How can you say 'all were 50:50'?
2. In #8, is the 4th coin toss not an independent event?

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.

OK. Lets work this through. Lets say I am sitting with you flipping this coin. We are betting 1$ each flip, you win on heads, I win on tails. So far, you have one 10 times, I have one 0. How "odd" is this? What is the probability of getting this odd result?

(.5)^10 = .0009765625

That is fine, looking backwards, and calling you a lucky bastard. But, I am foolish, thinking this NEXT flip, I must be do. No. The next flip I am wondering, what are my chances of getting a buck back?

.5

---------------------------------------------------------------------------------------

So. If I were a betting man, and I am, I would take the bet that you can't get 10 head in a row, and feel very comfortable. I would be much less interested in the 1$ per flip bet.

This make sense?

you do not have the answers for my two questions?




1. How can you say 'all were 50:50'?
You set the conditions. You said it was a "fair coin".

2. In #8, is the 4th coin toss not an independent event?
As I have said numerous times, each flip is an independent event, yes. Its possible I am not understanding your question here.

I think you are stuck on independent events and multiplication. P(A) P(B). Each independently has a .5 probability, but the problibity of intersection of the two is .25.

Flip one potential outcomes.
H T

Flip two potential outcomes.
H T

Flip 1 and 2 combined potential outcomes
(H T) (H T)
(.5)(.5)

OR put another way, I flip the coin twice this is what I can get
HH
HT
TT
TH

Out of that set, I see the .25 of getting exactly HH.

#8. has that we already have HH / TT three times in a row (a requirement to carry out the experiment) . It doesn't matter if the probability is 0.25

I am interested in that 4th coin toss.

Yea, you are just misunderstanding. Let me give it more more shot.

In the independent event of flipping a coin, you have these potential outcomes.
H or T

Each time you do it, you have the exact same potential outcomes.
H or T

You can do this 1 million times, the potential outcome is the same
H or T

Now, you want to talk about the potential outcomes for multiple flips. I did this above for two flips, I will do it again. Potential outcomes for TWO coin flips.
H and H
H and T
T and T
T and H

The is four potential outcomes of the union of the two. So. The probability of getting H and H is .25. The probability of getting heads on the first was .5 and .5 on the second. You could do this 1 million times and it would be .5^1000000 that you would get all heads, but each flip you only had two potential outcomes - H or T - .5.
Deb-8-A-Bull
Posts: 2,181
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3/14/2016 5:30:09 PM
Posted: 8 months ago
At 3/14/2016 5:13:39 PM, FillFueler wrote:
At 3/14/2016 5:03:26 PM, TBR wrote:
At 3/14/2016 4:43:09 PM, FillFueler wrote:
At 3/14/2016 4:32:32 PM, TBR wrote:
At 3/14/2016 4:18:50 PM, FillFueler wrote:
At 3/14/2016 4:01:47 PM, TBR wrote:
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

TBR-
1. How can you say 'all were 50:50'?
2. In #8, is the 4th coin toss not an independent event?

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.

OK. Lets work this through. Lets say I am sitting with you flipping this coin. We are betting 1$ each flip, you win on heads, I win on tails. So far, you have one 10 times, I have one 0. How "odd" is this? What is the probability of getting this odd result?

(.5)^10 = .0009765625

That is fine, looking backwards, and calling you a lucky bastard. But, I am foolish, thinking this NEXT flip, I must be do. No. The next flip I am wondering, what are my chances of getting a buck back?

.5

---------------------------------------------------------------------------------------

So. If I were a betting man, and I am, I would take the bet that you can't get 10 head in a row, and feel very comfortable. I would be much less interested in the 1$ per flip bet.

This make sense?

you do not have the answers for my two questions?




1. How can you say 'all were 50:50'?
You set the conditions. You said it was a "fair coin".

2. In #8, is the 4th coin toss not an independent event?
As I have said numerous times, each flip is an independent event, yes. Its possible I am not understanding your question here.

I think you are stuck on independent events and multiplication. P(A) P(B). Each independently has a .5 probability, but the problibity of intersection of the two is .25.

Flip one potential outcomes.
H T

Flip two potential outcomes.
H T

Flip 1 and 2 combined potential outcomes
(H T) (H T)
(.5)(.5)

OR put another way, I flip the coin twice this is what I can get
HH
HT
TT
TH

Out of that set, I see the .25 of getting exactly HH.

#8. has that we already have HH / TT three times in a row (a requirement to carry out the experiment) . It doesn't matter if the probability is 0.25

I am interested in that 4th coin toss.

The reason why your trying to get a example of more then 1 dice means your looking for a coin toss that was different then the way you got your 1st outcome. If you agree the 1st outcome is 50 / 50. How can it change
TBR
Posts: 9,991
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3/14/2016 5:42:43 PM
Posted: 8 months ago
At 3/14/2016 5:30:09 PM, Deb-8-A-Bull wrote:
At 3/14/2016 5:13:39 PM, FillFueler wrote:
At 3/14/2016 5:03:26 PM, TBR wrote:
At 3/14/2016 4:43:09 PM, FillFueler wrote:
At 3/14/2016 4:32:32 PM, TBR wrote:
At 3/14/2016 4:18:50 PM, FillFueler wrote:
At 3/14/2016 4:01:47 PM, TBR wrote:
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

TBR-
1. How can you say 'all were 50:50'?
2. In #8, is the 4th coin toss not an independent event?

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.

OK. Lets work this through. Lets say I am sitting with you flipping this coin. We are betting 1$ each flip, you win on heads, I win on tails. So far, you have one 10 times, I have one 0. How "odd" is this? What is the probability of getting this odd result?

(.5)^10 = .0009765625

That is fine, looking backwards, and calling you a lucky bastard. But, I am foolish, thinking this NEXT flip, I must be do. No. The next flip I am wondering, what are my chances of getting a buck back?

.5

---------------------------------------------------------------------------------------

So. If I were a betting man, and I am, I would take the bet that you can't get 10 head in a row, and feel very comfortable. I would be much less interested in the 1$ per flip bet.

This make sense?

you do not have the answers for my two questions?




1. How can you say 'all were 50:50'?
You set the conditions. You said it was a "fair coin".

2. In #8, is the 4th coin toss not an independent event?
As I have said numerous times, each flip is an independent event, yes. Its possible I am not understanding your question here.

I think you are stuck on independent events and multiplication. P(A) P(B). Each independently has a .5 probability, but the problibity of intersection of the two is .25.

Flip one potential outcomes.
H T

Flip two potential outcomes.
H T

Flip 1 and 2 combined potential outcomes
(H T) (H T)
(.5)(.5)

OR put another way, I flip the coin twice this is what I can get
HH
HT
TT
TH

Out of that set, I see the .25 of getting exactly HH.

#8. has that we already have HH / TT three times in a row (a requirement to carry out the experiment) . It doesn't matter if the probability is 0.25

I am interested in that 4th coin toss.

The reason why your trying to get a example of more then 1 dice means your looking for a coin toss that was different then the way you got your 1st outcome. If you agree the 1st outcome is 50 / 50. How can it change

Yea. The coin would have to change. The sample would have to have a new side or something. Its very simple logic, but I can understand his confusion.
FillFueler
Posts: 18
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3/14/2016 5:44:21 PM
Posted: 8 months ago
At 3/14/2016 5:20:11 PM, TBR wrote:
At 3/14/2016 5:13:39 PM, FillFueler wrote:
At 3/14/2016 5:03:26 PM, TBR wrote:
At 3/14/2016 4:43:09 PM, FillFueler wrote:
At 3/14/2016 4:32:32 PM, TBR wrote:
At 3/14/2016 4:18:50 PM, FillFueler wrote:
At 3/14/2016 4:01:47 PM, TBR wrote:
At 3/14/2016 3:46:03 PM, FillFueler wrote:
At 3/14/2016 3:35:18 PM, TBR wrote:
At 3/14/2016 3:30:44 PM, FillFueler wrote:
At 3/14/2016 2:34:32 PM, TBR wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
At 3/14/2016 9:15:03 AM, FillFueler wrote:
Is the probability for me to get a head still 0.5?
Welcome, FF.

If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.

You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.

Now see what happens to the coins in each pile when you flip a third time.

You know as we toss a coin again and again, the head - tail ratio comes closer to 0.5
The head - tail ratio or probability is more likely to be 1/2 (or closer to) if we flip the coin, say, 100 times rather than 50 times.

Now, if we do the same 10 times and get 8 heads, we are more likely to get a tail instead of head . This is true, you can experiment yourself RuvDraba. You can say, this brings the value of probability closer to half and justify that there is 50% chance - by violating the same theory.

This is the paradox. The cOin toss paradox.

Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.

Our previous observations are affecting the future outcomes. Practically, yes it is so.

You are talking probability vs statistics.

So you confess statistics affects probability? And below you are claiming probability is a constant. You better make up your mind.

PROBABILITY that you will get heads is always the same.

No not at all.

Probability is about predictions.

Again after reading below it seems like you are saying that statistics is about predictions, not probability and once again you have repeated that probability in the coin toss remains same. Your stance eliminates the only evidence probability can have that is statistics.

The probability in the coin toss will always have the same chance.

Statistics look backwards. If you look back over the data set of a 50:50 (like coin toss) you will get a normal distribution.

You seem vested in misreading this.

Each new coin toss has the exact same probability. It is an independent event. 50:50.

If you run a test, the data gathered will have a collection of events that all were 50:50.

TBR-
1. How can you say 'all were 50:50'?
2. In #8, is the 4th coin toss not an independent event?

If I add one more test to the dataset, the new test will still have the same probability.

-------------------------------------------------------------------------------------------------------

Do the test another way.

Make 10 sets of 10 coin tosses. Graph the total number of heads in each. The distribution will be a curve (Gaussian). That, however, will display the point well, that each coin toss is independent, and the statistical distribution is reflecting the initial probability.

OK. Lets work this through. Lets say I am sitting with you flipping this coin. We are betting 1$ each flip, you win on heads, I win on tails. So far, you have one 10 times, I have one 0. How "odd" is this? What is the probability of getting this odd result?

(.5)^10 = .0009765625

That is fine, looking backwards, and calling you a lucky bastard. But, I am foolish, thinking this NEXT flip, I must be do. No. The next flip I am wondering, what are my chances of getting a buck back?

.5

---------------------------------------------------------------------------------------

So. If I were a betting man, and I am, I would take the bet that you can't get 10 head in a row, and feel very comfortable. I would be much less interested in the 1$ per flip bet.

This make sense?

you do not have the answers for my two questions?




1. How can you say 'all were 50:50'?
You set the conditions. You said it was a "fair coin".

2. In #8, is the 4th coin toss not an independent event?
As I have said numerous times, each flip is an independent event, yes. Its possible I am not understanding your question here.

I think you are stuck on independent events and multiplication. P(A) P(B). Each independently has a .5 probability, but the problibity of intersection of the two is .25.

Flip one potential outcomes.
H T

Flip two potential outcomes.
H T

Flip 1 and 2 combined potential outcomes
(H T) (H T)
(.5)(.5)

OR put another way, I flip the coin twice this is what I can get
HH
HT
TT
TH

Out of that set, I see the .25 of getting exactly HH.

#8. has that we already have HH / TT three times in a row (a requirement to carry out the experiment) . It doesn't matter if the probability is 0.25

I am interested in that 4th coin toss.

Yea, you are just misunderstanding. Let me give it more more shot.

In the independent event of flipping a coin, you have these potential outcomes.
H or T

Each time you do it, you have the exact same potential outcomes.
H or T

You can do this 1 million times, the potential outcome is the same
H or T

Now, you want to talk about the potential outcomes for multiple flips. I did this above for two flips, I will do it again. Potential outcomes for TWO coin flips.
H and H
H and T
T and T
T and H

The is four potential outcomes of the union of the two. So. The probability of getting H and H is .25. The probability of getting heads on the first was .5 and .5 on the second. You could do this 1 million times and it would be .5^1000000 that you would get all heads, but each flip you only had two potential outcomes - H or T - .5.

OK TBR LISTEN -

Try to understand. We already have 3 tails in a row. Now why is the probability of getting a head is > 0.5

Try #8 yourself. I
TBR
Posts: 9,991
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3/14/2016 5:53:58 PM
Posted: 8 months ago
OK TBR LISTEN -

Try to understand. We already have 3 tails in a row. Now why is the probability of getting a head is > 0.5

Try #8 yourself. I

OK. Lets do it this way. What is the probability of getting 4 heads in a row.
(.5) * (.5) * (.5) * (.5) = .0625

Each toss, 1 - 4, had only two potential outcomes (H or T). That is .5. So, you asked "what is the chance flip 4 will be heads". The answer is 50/50.

That work for you?
FillFueler
Posts: 18
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3/14/2016 6:03:43 PM
Posted: 8 months ago
At 3/14/2016 4:50:52 PM, RuvDraba wrote:
At 3/14/2016 2:12:36 PM, FillFueler wrote:
At 3/14/2016 9:34:32 AM, RuvDraba wrote:
If the result of each coin toss is independent, then by definition the coin has no memory. Your chance of another head remains 0.5.
You can test this empirically. Set out (say) sixteen coins in a line, flip each and separate the coins into a 'Heads' pile and a 'Tails' pile. Flip again, and separate each pile into two more piles, so that you now have four piles: H-H, H-T, T-H, T-H.
Toss a coin. First, get (say) 3 tails and NOW note whether or not the probability of getting a head or tail is still half. Anyone can do this. As long as I am getting more heads than tails ( after observing 3 tails) , there is a problem.
Do you believe that the experiment I proposed is substantially different to the experiment you proposed?

For example, if I start with 32 coins, toss them, and begin creating piles reflecting the outcomes, then after three tosses per coin, we will likely have eight outcomes piles:
HHH HHT HTH HTT THH THT TTH TTT

Since there are eight ordered outcomes, all equally likely, we should have around four coins in each pile.

Now, let's keep only the HHH pile with its four or so coins. Toss them each again. That will repeat your HHH experiment approximately four times, yes?

What do you predict will happen to that pile?

there is <50% chance that those coins are going to make it in the HHHH pile.