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: 6 live in the town of gaston, 2 live in pike, and 2 live in wells. two winners will be selected at random. what is the probability that the first winner lives in gaston and the second lives in pike? 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 Gaston is the number of Gaston customers divided by the total number of customers. There are 6 Gaston customers and 10 total customers. $P(\text{first in Gaston})=\frac{6}{10}$
Step2: Calculate probability of second - winner
After one customer is selected as the first - winner, there are 9 customers left. There are 2 Pike customers. So the probability that the second winner lives in Pike given that the first winner lives in Gaston is $\frac{2}{9}$.
Step3: Calculate joint probability
For dependent events, the probability that the first winner lives in Gaston and the second lives in Pike is the product of the probabilities of each event. $P = \frac{6}{10}\times\frac{2}{9}=\frac{12}{90}=\frac{2}{15}$
Answer:
$\frac{2}{15}$