Well I don't know about statistics but my mom has bipolar disorder and growing up with that can make you feel a bit neglected and confused. I don't yet know if I have it but I have suffered from depression and am a schizoid. Just let the kid know what's going on and that it's not their fault.
Not exactly 50/50, but there is still a ridiculous amount of research being conducted on this very question. Studies have suggested that bipolar disorder has been linked to certain genes (which may be different in each family, or may be a collaborative effect of many specific genes working together in just the right/wrong way to make a person bipolar, so to speak).
To keep it simple, you have a 50/50 chance of passing these genes along to your child, which would then PREDISPOSE him/her to being bipolar. It doesn't necessarily mean it'll be expressed in them. Lots of people are carriers for the gene/trait, but never actually have bipolar disorder. The risks are increased of course if the child's mother and father are BOTH bipolar. If it makes you feel any better though, that 50/50 chance thing gets "reset" every time... So if this child ends up not being bipolar, it doesn't necessarily mean the next one will be. (I bring that up because of 3 children bbm1188 was speaking of). =)
I read that Its 50/50. Depends though, I know ppl that are bipolar and have three kids, one has mood disorder. I'm bipolar, so is my husband and were having a baby in Nov. So I'm curious to see how this will work out. Either way what better people to help a child or someone deal with it then someone who actually has it themselves.