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]