the original question is like this:
In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same)
The answer is easy as 1:1 if you model it as a geometric distribution.
Here comes the modified version:
In a country where everyone wants a boy, each family continues having babies till they have a boy or they have ten girls. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same)
Can someone shed some light on how to attack this problem?
Best Answer
HINT: Imagine that you flip a fair coin $10$ times. Your score is the number of times tails comes up before the first head, or $10$ if all $10$ flips come up tails. Your opponent’s score is $1$ if you get a head at least once and $0$ otherwise. What is your expected score? What is your opponent’s expected score?