Question

At Sally's Hair Salon there are three hair stylists. 28% of the hair cuts are done by Chris, 30% are done by Karine, and 42% are done by Amy. Chris finds that when he does hair cuts, 4% of the customers are not satisfied. Karine finds that when she does hair cuts, 5% of the customers are not satisfied. Amy finds that when she does hair cuts, 5% 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?

Answer 1

Answer:

0.4449 or 44.49%

Step-by-step explanation:

The total probability of customer not leaving satisfied is given by the sum of the product of the probability of each stylist doing a hair cut by the probability of the customer not being satisfied with the cut:

$P(N) =0.28*0.04+0.30*0.05+0.42*0.05 = 0.0472$

The probability of Amy doing a hair cut given that the customer was not satisfied is:

$P(A|N) =\frac{0.42*0.05}{0.0472} \\P(A|N) = 0.4449 =44.49\%$