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, 3 live in Pike, and 5 live in Wells. Two winners will be selected at random. What is the probability that the first winner lives in Pike and the second lives in Wells? Write your answer as a fraction in simplest form.

Answer 1

The probability that the first winner lives in Pike and the second winner lives in Wells is 1/6.

Step-by-step explanation:

To calculate the probability that the first winner lives in Pike and the second lives in Wells, we need to find the individual probabilities of each event happening and then multiply them together as they are independent events.

The probability that the first winner lives in Pike is 3 out of 10, since there are 3 residents from Pike out of a total of 10 participants. This can be written as 3/10.

After the first winner is chosen, we are left with 9 participants, assuming that the same person cannot win twice. The probability that the second winner lives in Wells, given the first is from Pike, is therefore 5 out of 9, as there are still 5 residents from Wells out of the remaining 9 participants. This is written as 5/9.

To find the overall probability of both events occurring, we multiply the two probabilities together: (3/10) × (5/9) = 15/90, which simplifies to 1/6.

So, the probability that the first winner lives in Pike and the second winner lives in Wells is 1/6.

Answer 2

The way to find probability is to add all of them together so 10
There are 3 in Pike so the probability is 3/10 Now you remove them I assume. If so then the answer is if the second lives in Wells the answer would be 5/9 if the winner is not removed which I assume is not the case then it would be 5/10 or 1/2