Of course not. When you make a Facebook account, you should be fully aware that everything you post there is going to be seen around the world. The word private doesn't even belong in Facebook. That is the whole point of the website: to share things with people around the world.
Facebook is not a place where information remains private, so one should not expect anything that is posted on there to remain private. Any information that is posted on there is shared with someone, whether it is friends, family, or random strangers and you can not control what these people do with that information. Even if you have very strict privacy settings anything posted can easily be shared between friends or family, It is illogical that anything posted on Facebook would remain private.
If you have a lot of friends that are able to view your posts then it won't matter if they can share it or tag it they can still tell what they seen by word of mouth. There is also the possibility that your account could be hacked, which would make your posts not private.
Facebook has made it pretty clear that you can't really expect any security or privacy from them. Also, once something is on the internet it's out there forever. Your friends have seen it and they can do what they like with it. If you put something on the internet, you really have no expectation of privacy, facebook included!