Answer to Question #192556 in Macroeconomics for john muhia

Question

One-fourth of the married couples in a far-off society have exactly three children. The other three-fourths of couples continue to have children until the first boy and then cease childbearing. Assume that each child is equally likely to be a boy or girl. What is the probability that the male line of descent of a particular husband will eventually die out?

Answer 1

To find the probability that the male line of descent of a particular husband will eventually die out.

$p(x=1)=\frac{3}{4}\times3\times(\frac{1}{2})^3=\frac{9}{32}\\p(x=2)=\frac{3}{4}\times 3 \times(\frac{1}{2})^3=\frac{9}{32}\\p(x=3)=\frac{3}{4}\times(\frac{1}{2})^3=\frac{3}{32}$

therefore the required probability is

$p(x=0)=1-[p(x=1)+p(x=2)+p(x=3)]\\=1-[\frac{9}{32}+\frac{9}{32}+\frac{3}{32}\\=\frac{11}{32}$