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 Population control (Posted on 2002-05-05)
In one nation, having a daughter is traditionally prefferable to having a son. Therefore, a couple will continue to have children until a daughter is born. Once they have a daughter, they will stop. (Assume that it is possible for a couple to have an unlimited number of children)

If the chance of a boy or a girl being born is equal, what would be the ratio boys to girls in this country?

 Submitted by levik Rating: 3.5714 (7 votes) Solution: (Hide) Assume the country has N families. Since every family will have children until a daughter is born, they will have N daughters. But there is a 1/2 chance that the first child will be a boy, making for N/2 "firstborn" boys. There is also a 1/4 chance that the second child will be a boy as well, for a total of N/2 + N/4 boys among the first- and second-born. It is easy to see that after each child, the chance that all the children are boys is reduced by 1/2, so the total number of boys is equal to N/2 + N/4 + N/8 + ..., an infinite series that adds up to N. So the ratio of boys/girls in the country will actually be 1 to 1, unaffected by the strange custom.

 Subject Author Date answer K Sengupta 2007-04-15 13:53:44 The word "equal" and more rants Mike 2005-05-09 23:29:54 re: Simple solution ajosin 2005-03-04 01:29:01 umm Vito 2003-09-06 16:12:04 Simple solution Federico Kereki 2003-07-27 05:11:05 Rrg Hard Matthew Bobbins 2003-02-27 10:19:57 re(3): Wasn't it obvious? levik 2002-07-09 04:30:34 re(2): Wasn't it obvious? TomM 2002-07-08 22:01:20 re: Wasn't it obvious? levik 2002-07-08 08:20:58 haha nice qball 2002-07-06 23:05:47 Wasn't it obvious? TomM 2002-05-10 22:55:50 thats the same answer theBal 2002-05-07 07:52:44 solution..I think btrnviagra 2002-05-07 00:55:15 one half theBal 2002-05-06 17:42:41

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