Question

Probability of dependent events2/5EspanolA department store is holding a drawing to give away free shopping sprees. There are 9 customers who have entered the drawing: 5 live in the town of Gaston,2 live in Pike, and 2 live in Wells. Two winners will be selected at random. What is the probability that both winners live in Gaston? Write your answer as afraction in simplest form.0DOХ5?

Answer 1

Given there are 9 customers who have entered the drawing, 5 live in the town of Gaston, 2 live in Pike, and 2 live in wells. Two winners will be selected at random.

We have to find the probability that both winners live in Gaston.

The probability that the first winner selected is from Gaston is:

`P(A)=(5)/(9)`

The probability that the second winner selected is from Gaston is:

`P(B|A)=(4)/(8)=(1)/(2)`

The probability that both winners live in Gaston is:

`\begin{gathered} P(A\cap B)=P(A)\cdot P(B|A) \\ =(5)/(9)\cdot(1)/(2) \\ =(5)/(18) \end{gathered}`

Thus, the answer is 5/18.