A dot-com company ships products from three different warehouses (A, B, and C). Based on customer complaints, it appears that 3% of the ship

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A dot-com company ships products from three different warehouses (A, B, and C). Based on customer complaints, it appears that 3% of the shipments coming from A are somehow faulty, as are 5% of the shipments coming from B, and 2% coming from C. suppose a customer is mailed an order and calls in a complaint the next day. What is the probability the item came from Warehouse C

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  1. Answer:

    The probability of getting defective product from warehouse C is 0.3448

    Step-by-step explanation:

    Missing question “Assume that Ware houses A, B and C ship 30%, 20% and 50% of the dot-com’s sales respectively.

    P(A) = Probability of product that comes from warehouse A

    P(B) = Probability of product that comes from warehouse B

    P(C) = Probability of product that comes from warehouse C

    P(A) =  30% = 0.30, P(B) =  20% = 0.20, P(C) =  50% = 0.50

    Let D denotes the number of defective products

    P(D|A) = 3% = 0.03

    P(D|B) = 5% = 0.05

    P(D|C) = 2% = 0.02

    The probability of getting defective product from warehouse C is as below using the Bayes Rule

    P(C|D) = P(D|C) P(C) / P(D|A)P(A) + P(D|B)P(B) + P(D|C)P(C)

    P(C|D) = 0.02 * 0.50 / (0.03*0.30) + (0.05*0.20) + (0.02*0.50)

    P(C|D) = 0.01 / 0.009 + 0.01 + 0.01

    P(C|D) = 0.01 / 0.029

    P(C|D) = 0.3448

    Therefore the probability of getting defective product from warehouse C is  0.3448.

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