ABC Company purchases electronic chips from three individual suppliers. Hall Ele

Question

ABC Company purchases electronic chips from three individual suppliers. Hall Electronics, Schuler Sales and Crawford Components. The probability ABC Company will use Hall electronics is 30%. uses Schuler Sales is 20%, and Crawford Components is 50%. While all three suppliers arc very reliable, the probability Hall Electronics products defective chips is 3%, the probability Schuler Sales and Crawford components produce defective chips is 5% and 4% respectively. ABC Company purchases electronic chips. What is the probability the electronic chips arc defective?

Explanation / Answer

Let Bi denote an electronic chip comes from supplier i(i = 1 for Hall, 2 for Schuler and 3 for crawford).

P(B1) = 0.3, P(B2) = 0.2, P(B3) = 0.5

Let D denote the event that an electronic chip is defective.
P(D|B1) = 0.03, P(D|B2) = 0.05, P(D|B3) = 0.04

P(D) = P(B1)*P(D|B1) + P(B2)*P(D|B2) + P(B3)P(D|B3) = 0.3*0.03 + 0.2*0.05 + 0.5*0.04 = 0.039

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