Unless you LINK to your Facebook account - and share updates - they should not. However, what if somebody that answers your question is linked to THEIR Facebook account? Then your question MAY show up on THEIR Facebook page. Scary, huh?
The thing is, there is NO privacy on the internet and posting anything 'personal' on ANY site is highly risky. Questions and answers from Yahoo Answers are 'stripped' and used on MANY other sites - and not all of them use the nice, private 'nicknames' we've given ourselves to hide behind here. Some show up with our email addresses; some with our REAL names. Even more scary.
So, while it is too late for what you have already posted, you should really bear this in mind for the future. After all, do you want your boss, your husband or your children - to do google search some day and see what you've posted? EEK!
