what is the probability that both customer selected are gaston residents

Question

A department store is holding a drawing to give free shopping sprees to two lucky customers. There are
14

customers who have entered the drawing:
5

live in the town of Gaston,
5

live in Pike, and
4

live in Wells. In the drawing, the first customer will be selected at random, and then the second customer will be selected at random from the remaining customers. What is the probability that both customers selected are Gaston residents?

Answer 1

The probability of a Gastonian on the first pick is 5/14.

The probability of a Gastonian on the second pick is 4/13.

Overall probability = 5*4/(14 * 13) = 10/91.

 

Another way to think of it uses the hypergeometric distribution and gets the same result: ₅C₂ / ₁₄C_{2, where} 

nC_{r is the binomial coefficient of n pick r.}