Problem 2. The local barber shop is home to three barbers. The barbers appear identical but...

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Problem 2. The local barber shop is home to three barbers. The barbers appear identical but vary in their ability to provide good haircuts. Denote the event that you receive a good haircut by G, the event that you do not receive a good haircut by NG, and the event that your hair is cut by barber i by B, where i = {1,2,3}. The probability that any particular barber cuts your hair is 1/3. The probability that you receive a good haircut from barber 1 is 1. The probability that you receive a good haircut from barber 2 is 1/2. The probability that you receive a good haircut from barber 3 is x, where x lies in the interval [0,1]. - Recall: Let A1, A2,..., A are disjoint and exhaustive events in the sample space S, such that P(A) > 0, let B be an event such that P(B) > 0. Then, P(B) = P(B|A)P(A) (Law of Total Probability) i-1 a. Assume P(NG) = 1. Find x. b. Calculate the probability that your hair is cut by barber 1 given that you received a good haircut. c. Calculate the probability that your hair is cut by barber 3 given that you received a bad haircut. Problem 2. The local barber shop is home to three barbers. The barbers appear identical but vary in their ability to provide good haircuts. Denote the event that you receive a good haircut by G, the event that you do not receive a good haircut by NG, and the event that your hair is cut by barber i by B, where i = {1,2,3}. The probability that any particular barber cuts your hair is 1/3. The probability that you receive a good haircut from barber 1 is 1. The probability that you receive a good haircut from barber 2 is 1/2. The probability that you receive a good haircut from barber 3 is x, where x lies in the interval [0,1]. - Recall: Let A1, A2,..., A are disjoint and exhaustive events in the sample space S, such that P(A) > 0, let B be an event such that P(B) > 0. Then, P(B) = P(B|A)P(A) (Law of Total Probability) i-1 a. Assume P(NG) = 1. Find x. b. Calculate the probability that your hair is cut by barber 1 given that you received a good haircut. c. Calculate the probability that your hair is cut by barber 3 given that you received a bad haircut.