## Thursday, August 07, 2008

### Boys or Girls

In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country?

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I say it is 50/50 because no matter how many babies you have, the likelihood of having a boy is 50%, so no matter when you start or stop having children, the ratio is 1:1

ReplyDeleteAnon, your logic is right on. For a more mathematically rigorous explanation, the key here is to consider all the different cases and their respective probabilities. The family will have n children, some number of girls before then a boy, and P(n) is the probability of that case. The expected value for any probability density function is the sum over all n of n*P(n).

ReplyDeleteP(1) = 1/2

P(2) = 1/4

P(3) = 1/8

P(4) = 1/16

So, n-bar (expected value for n) is:

1/2+2/4+3/8+4/16+... = 2

That means the average value for number of children is 2, one of which is a boy. So yes, it's still 50/50. Crazy how math works and stuff...

As always Abe, a great explanation.

ReplyDeletei do feel the urge to chime in that the Y sperm is lighter than the X sperm since it's missing 800 or so genes and therefore the chance of having a male child concieved is increased but the chance of a male child miscarraige (cause the mother's body recognizes a flaw in the child due to missing genes) is also increased. More male babies are born that female, but more females live to a ripe old age than males because of superior genetics. (please don't take this as sexist)

ReplyDelete