Answer:
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.