a department store is holding a drawing to give away free shopping sprees. there are 10 customers who have…
a department store is holding a drawing to give away free shopping sprees. there are 10 customers who have entered the drawing: 4 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 the first winner lives in wells and the second lives in gaston? write your answer as a fraction in simplest form.
Answer
Explanation:
Step1: Calculate probability of first - winner
The probability that the first winner lives in Wells is the number of customers from Wells divided by the total number of customers. There are 4 customers from Wells and 10 total customers. So the probability $P_1=\frac{4}{10}$.
Step2: Calculate probability of second - winner
After one customer is selected (the first - winner from Wells), there are 9 customers left. There are 4 customers from Gaston. So the probability that the second winner lives in Gaston given that the first winner is from Wells is $P_2 = \frac{4}{9}$.
Step3: Calculate combined probability
Since these are independent - like (in the sense of sequential selection) events, the probability that the first winner lives in Wells and the second lives in Gaston is the product of the two probabilities. So $P = P_1\times P_2=\frac{4}{10}\times\frac{4}{9}=\frac{16}{90}=\frac{8}{45}$.
Answer:
$\frac{8}{45}$