Answer:
The probability of getting defective product from warehouse C is 0.3448
Step-by-step explanation:
<em>Missing question </em><em>"Assume that Ware houses A, B and C ship 30%, 20% and 50% of the dot-com's sales respectively.</em>
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<em>P(A) = </em>Probability of product that comes from warehouse A
<em>P(B) = </em>Probability of product that comes from warehouse B
<em>P(C) = </em>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.
