Chapter 16.4, Problem 16P

Due to its high population, China has a stringent policy on having children. In rural China, couples are allowed to have either 1 or 2 children according to the following rule: If their first child is a boy, they are not allowed to have any more children. If their first child is a girl, then they are allowed to have a second child. Let’s assume that all couples follow this policy and have as many children as the policy allows.
a. Do you think this policy will result in more boys, more girls, or about the same number of boys as girls being born? (Answer without performing any calculations—just make a guess.)
b. Now consider a random group of 100,000 rural Chinese couples who will have children. Assume that any time a couple has a child the probability of having a boy is $\frac{1}{2}$ .

i. In the ideal, how many couples will have a boy as their first child, and how many will have a girl as their first child?
ii. In the ideal, of those couples who have a girl first,how many will have a boy as their second childand how many will have a girl as their secondchild?
iii. Therefore, overall, what fraction of the childrenborn in rural China under the given policy shouldbe boys and what fraction should be girls?