Use Bayes' theorem to find the indicated probability.
-At Sally's Hair Salon there are three hair stylists. 23% of the hair cuts are done by Chris, 32% are done by Karine, and 45% are done by Amy.
Chris finds that when he does hair cuts, 7% of the customers are not satisfied. Karine finds that when she does hair cuts, 8% of the customers are not satisfied.
Amy finds that when she does hair cuts, 3% of the customers are not satisfied.
Suppose that a customer leaving the salon is selected at random. If the customer is not satisfied, what is the probability that their hair was done by Amy?
A) 0.245
B) 0.324
C) 0.03
D) 0.292

Question

Quizplus · Accepted Answer

The probability that a customer is not satisfied with their haircut is:P(not satisfied) = 0.07 * 0.23 + 0.08 * 0.32 + 0.03 * 0.45 = 0.046The probability that a customer's hair was done by Amy given that they are not satisfied is:P(Amy | not satisfied) = P(not satisfied | Amy) * P(Amy) / P(not satisfied)= 0.03 * 0.45 / 0.046 = 0.292

Use Bayes' Theorem to Find the Indicated Probability