A department store is holding a drawing to give away free shopping sprees. There are 9 customers who have entered the drawing: 2 live in the town of Gaston, 5 live in Pike, and 2 live in Wells. Two winners will be selected at random. What is the probability that the first winner lives in Gaston and the second lives in Pike? Write your answer as a fraction in simplest form.
There are a total of 9 customers entered in the drawing. For the first winner to be from Gaston, there are 2 possible winners out of 9 customers. For the second winner to be from Pike, there will be 5 possible winners out of 8 customers remaining (since one has already been chosen). Therefore, the probability is:
(2/9) * (5/8) = 10/72 = 5/36
So the probability that the first winner lives in Gaston and the second lives in Pike is 5/36.