Question

A department store is holding a drawing to give away free shopping sprees. There are 10 customers who

have entered the drawing: 2 live in the town of Gaston, 2 live in Pike, and 6 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.

Answer 1

We need to find the probability that the two winners line in Pike.

We know that 2 out of the 10 customers who entered the drawing live in Pike.

Thus, the probability of the first winner line in Pike is:

`(2)/(10)`

Then, considering the first winner live in Pike, there are left 9 customers, and 1 of them live in Pike. Thus, the probability that the second winner lives in Pike is:

`(1)/(9)`

Now, the probability that the first one lives in Pike and the second one also lives in Pike is the product of the two probabilities we found:

`(2)/(10)*(1)/(9)=(2)/(10*9) =(1)/(10*4.5) =(1)/(45)`

Therefore, the probability that both winners live in Pike is:

`(1)/(45)`