At Sally’s Hair Salon there are three hair stylists. 22% of the haircuts are done by Chris, 30% are done by Karine, and 48% are done by Amy.

Question

At Sally’s Hair Salon there are three hair stylists. 22% of the haircuts are done by Chris, 30% are done by Karine, and 48% are done by Amy. Chris finds that when he does haircuts, 5% of the customers are not satisfied. Karine finds that when she does haircuts, 3% of the customers are not satisfied. Amy finds that when she does haircuts, 7% 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 Chris

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Helga 4 years 2021-08-21T20:54:02+00:00 1 Answers 81 views 0

Answers ( )

  1. thienthanh
    0
    2021-08-21T20:55:30+00:00
    Reply

    Answer:

    0.2052 = 20.52% probability that their hair was done by Chris

    Step-by-step explanation:

    Conditional Probability

    We use the conditional probability formula to solve this question. It is

    P(B|A) = \frac{P(A \cap B)}{P(A)}

    In which

    P(B|A) is the probability of event B happening, given that A happened.

    P(A \cap B) is the probability of both A and B happening.

    P(A) is the probability of A happening.

    In this question:

    Event A: Customer not satisfied

    Event B: Hair done by Chris.

    Probability of a customer not being satisfied.

    5% of 22%(Chris)

    3% of 30%(Karine)

    7% of 48%(Amy)

    This means that:

    P(A) = 0.05*0.22 + 0.03*0.3 + 0.07*0.48 = 0.0536

    Probaility of a customer not being satisfied and hair done by Chris:

    5% of 22%. So

    P(A \cap B) = 0.05*0.22 = 0.011

    What is the probability that their hair was done by Chris?

    P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.011}{0.0536} = 0.2052

    0.2052 = 20.52% probability that their hair was done by Chris

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