Please explain Surf City has a population of 300 people incl

Surf City has a population of 300 people, including 200 girls and 100 boys. Suppose that 70 of the girls have Brown hair If X is a person randomly chosen from the population, the events \"X has brown hair\" and \" X is a boy\" are independent. How many boys in Surf City have brown hair?

Solution

Let

H = has brown hair
B = boy
G = girl

Thus, as H and B are independent, then

P(H|B) = P(H|G)

Thus,

P(H|B) = 70/200 = 0.35

Thus,

P(B n H) = P(B) P(H|B) = (100/300)*0.35 = 35 [ANSWER, 35 boys have brown hair]