Only One Boy, But As Many As Infinite Girls, and it... equal out?

Transcript

is it possible for us to intentionally create a gender gap in our scenario there is equal probability of having a boy or a girl also we're going to say these are independent events so having a boy one time doesn't influence whether you'll have a boy or girl the next time and finally the stopping rule after mothers have just one boy they will stop having children forever every time now let's review the possible sequence of births right off the bat there's a 50/50 chance they just have a boy and then have no more kids but they also have one girl two girl three however many in each case there will be one boy but the number of girls will vary by a lot to calculate the number of girls in each family we can use the concept of expected value where e to the G is the number of expected girls in each family this is an infinite geometric Series where the probability of having zero girls is 1/2 the probability of having one girl is a quarter and this series converges to one which means the average number of girls and boys in the house will both be one which means the long-term ratio will be 1: one