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 both winners live in Gaston? answer as a fraction in simplest form.

Answer 1

`(1)/(45)`

Explanation:

In order to get the probability of both winners living in Gaston we would need to multiply the probability of the first winner being from Gaston by the probability of the second winner being from Gaston (taking into the count the fact that the first winner was from Gaston). Now we need to find both of this probabilities.

As we know a probability is basically the number of outcomes that you want/need, divided by the number of all possible outcomes. This means that probably of the first winner being from Gaston is
`(2)/(10)` (since there is 2 people living in Gaston, and 10 people entered the drawing). If we simplify we get
`(1)/(5)`.

Now when finding the probability of the second winner being from Gaston we get
`(1)/(9\\)` (since the first winner was from Gaston we now have only 1 from Gaston and there is now 9 customers in the drawing).

Finally we just multiply both of this probabilities to get the probability of both winners living in Gaston.

(
`(2)/(10)`)(
`(1)/(9)`) =
`((2)(1))/((10)(9))`=
`(2)/(90)` =
`(1)/(45)`