Consider a couple that has decided to have children. They will continue having children until they have more girls than boys. What is the expected number of children they will have?

  • $\begingroup$ See this near duplicate $\endgroup$
    – lulu
    Sep 18 at 21:35
  • $\begingroup$ similar but different $\endgroup$
    – Jason
    Sep 18 at 22:05
  • $\begingroup$ Focus only on the odd numbered births. That is, if, after $~2n~$ births, there are more girls than boys, then there must be at least two more girls than boys. This is because $~2n~$ is an even number, so the number of girls and number of boys (that sum to $~2n~$) must have the same odd even parity. So, you would then conclude that after $~2n-1~$ births there (still) must have been more girls than boys. $\endgroup$ Sep 18 at 22:05
  • $\begingroup$ The same argument works in this case with minimal changes. $\endgroup$
    – lulu
    Sep 18 at 22:10
  • $\begingroup$ There are also questions like math.stackexchange.com/q/1986723/139123 that deal with the same problem in a more abstract way. $\endgroup$
    – David K
    Sep 18 at 23:27


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