Question

An event has 50 female contestants and 13 male contestants. A random sample of 12 contestants is drawn. What is the probability that exactly 8 of the contestant will be female?

Answer 1

p(female) $= \frac{50}{50+13} = 0.79$

n=12

x=8

Binomial distribution

$P(X=x) = C^{12}_x(0.79)^x(1-0.79)^{12-x} \\ P(X=8) = C^{12}_8(0.79)^8(1-0.79)^{12-8} \\ = 495 \times 0.79^8 \times 0.21^4 \\ = 495 \times 0.15171 \times 0.001944 \\ = 0.14598$