Find Pr [𝑋=2] .

Question

There are 4 women and 2 men waiting on standby for a flight to New York. Suppose that 3 of these 6 people are chosen at random for the flight. If the random variable 𝑋 counts the number of women chosen. Find Pr [𝑋=2] .

Answer 1

Total possible outcomes is C(6, 3). Positive outcames C(3, 2),

So, Pr(X = 2) = C(3,2)/C(6,3) = [3!/(2!1!)]/[6!/(3!3!)] = 3/20

Answer 2

This is a classic hypergeometric question.

The answer is ₄C₂ * ₂C₁ / ₆C₃ = .8