Question

N 342 42. In most countries the ratio of boys to girls is about 1.04 to 1. Find the probability that a family in one these countries with exactly 6 children will have at least 3 boys? (Ignore the probability of multiple births.)

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

P(boy), p = 1.04/(1+1.04) = 0.5098

q = 1 - p = 0.4902

n = 6

P(at least 3 boys) = P(3) + P(4) + P(5) + P(6)

= 6C3x0.5098³x0.4902³ + 6C4x0.5098⁴x0.4902² + 6C5x0.5098⁵x0.4092 + 0.5098⁶

= 0.3121 + 0.2435 + 0.1013 + 0.0176

= 0.6745