Gender Probabilities for Twins
Date: 08/27/2006 at 13:17:09 From: Melissa Subject: Twin gender probability Hi Doctor Math. I am pregnant with twins--sex unknown. Since neither is older than the other, what is the probability of having any gender combination? I remember from college genetics that each birth is mutually exclusive, therefore the probability of any combination of boy or girl is 1/2, i.e. each child will either be a boy or a girl. My husband is using the bb, gg, bg, gb theory of probability, and that would increase the odds of having a boy and a girl to 1/2, while having a bb or gg would be 1/4. My point is that bg and gb are the same combination, so his probability isn't correct. What do you think? I saw your string on a similar question, but it doesn't address twin births, and I wanted to be certain that I was thinking about this correctly. Thanks!
Date: 08/27/2006 at 21:13:40 From: Doctor Peterson Subject: Re: Twin gender probability Hi, Melissa. As a twin myself (and my identical twin brother is also a Math Doctor), I HAVE to take this question! If there were only fraternal twins, then your husband would be right. Even with twins, you can distinguish them (firstborn/secondborn, favorite/nonfavorite, or whatever), so BG and GB are not the same. As an example, I was expected to be a girl (because my heartbeat was weaker, and they didn't have ultrasound yet). We could be distinguished, that is, even without knowing which was a boy and which was a girl or what our names would turn out to be. So you could make up a table of the four equally likely cases: Dave | boy | girl| ----+-----+-----+ boy | 1/4 | 1/4 | Rick ----+-----+-----+ girl| 1/4 | 1/4 | ----+-----+-----+ That gives probablities of 1/4 (two boys), 1/4 (two girls), 1/2 (one of each). Now in reality, you also have to bring in the probability that the twins turn out to be identical--in which case they MUST both be the same sex. (I understand there are other odd possibilities, but I'll neglect those.) Suppose the probability of having fraternal twins is F, and of having identical twins is I. Then, given that you have twins, the probabilities of their being identical is I/(F+I); we end up with this table: BB BG GB GG I I Identical ------ ------ 2(F+I) 2(F+I) F F F F Fraternal ------ ------ ------ ------ 4(F+I) 4(F+I) 4(F+I) 4(F+I) So the probability of two boys, or of two girls, is 2I + F ------ 4(F+I) and the probability of one of each is F ------ 2(F+I) A couple sites I looked at said that F = 1/125 and I = 1/300. Another site said that 1/3 of all twins are identical. Others give different numbers. If I take that first pair of numbers, we get the probability of two boys, or of two girls, is 0.3235, and the probability of one of each is 0.3529. So each probability is about 1/3. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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