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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Tundexi Tundexi · Answer 1 · 2020-09-25T04:39:46+02:00

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.