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A department store is holding a drawing to give away free shopping sprees. There are 9 customers who have entered the drawing: 3 live in the town of Gaston, 2 live in Pike, and 4 live in Wells. Two winners will be selected at random. What is the probability that both winners live in Pike? Write your answer as a fraction in simplest form.

Sagot :

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

We know that 2 out of the 9 customers who entered the drawing live in Pike.

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

[tex]\frac{2}{9}[/tex]

Then, considering the first winner live in Pike, there are left 8 customers, and 1 of them live in Pike. Thus, the probability that the second winner lives in Pike is:

[tex]\frac{1}{8}[/tex]

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:

[tex]\frac{2}{9}\times\frac{1}{8}=\frac{2}{9\times8}=\frac{1}{9\times4}=\frac{1}{36}[/tex]

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

[tex]\frac{1}{36}[/tex]

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