Question

At Sally's Hair Salon there are three hair stylists. 33% of the hair cuts are done by Chris, 37% are done by Karine, and the rest are done by Amy. Chris finds that when he does hair cuts, 5% of the customers are not satisfied. Karine finds that when she does hair cuts, 7% of the customers are not satisfied. Amy finds that when she does hair cuts, 1% 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? Express your answer as a percentage rounded to the nearest hundredth.

Answer 1

Answer:

Given,

To determine the probability that their hair was done by Amy

Bayes' Theorem: P(A | B) = P(A and B)/P(B)

P(customer isn't fulfilled) = P(hair was finished by Chris and client isn't fulfilled) + P(hair was finished by Karine and client isn't fulfilled) + P(hair was finished by Amy and client isn't fulfilled)

substitute values

= 0.33*0.05 + 0.37*0.07 + 0.30*0.01

= 0.0165 + 0.0259 + 0.003

= 0.0454

P(hair was finished by Amy | client isn't fulfilled) = P(hair was finished by Amy and client isn't fulfilled)/P(customer isn't fulfilled)

substitute values

= 0.30*0.01 / 0.0454

= 0.0661