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?
5
-
$\begingroup$ See this near duplicate $\endgroup$– luluSep 18 at 21:35
-
$\begingroup$ similar but different $\endgroup$– JasonSep 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. $\endgroup$– user2661923Sep 18 at 22:05
-
$\begingroup$ The same argument works in this case with minimal changes. $\endgroup$– luluSep 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 KSep 18 at 23:27
Add a comment
|