Question

20 POINTS!

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, 2 live in Pike, and 5 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 the simplest form.

Answer 1

There are a total of 9 customers who have entered the drawing. The probability that the first winner lives in Gaston is 2/9, since there are 2 customers from Gaston out of 9 total customers.

Once the first winner is selected, there will be 8 customers remaining, out of which 2 live in Pike. Therefore, the probability that the second winner lives in Pike, given that the first winner lives in Gaston, is 2/8 or 1/4.

To find the probability that the first winner lives in Gaston and the second winner lives in Pike, we need to multiply the probabilities of the two events:

P(Gaston first and Pike second) = P(first winner from Gaston) * P(second winner from Pike, given that first winner is from Gaston)

P(Gaston first and Pike second) = (2/9) * (1/4)

P(Gaston first and Pike second) = 2/36

Therefore, the probability that the first winner lives in Gaston and the second winner lives in Pike is 2/36, which simplifies to 1/18.