Question

From families with two children a family is chosen at random. Let X be the number of girls in the family. Find P(X>0). Assume that in a two child family all gender distributions are equally probable.

Answer 1

Since the random variable X has binomial distribution with p = q = 1/2 = 0.5, n = 2:

$P(X > 0 ) = 1 - P(X = 0) = 1 - q^n = 1 - 0.5^2 = 1 - 0.25 = 0.75$

Answer: P(X>0) = 0.75