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 are 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 are defective?

Explanation / Answer

P(hall electronics) = 0.3

P(schuler scales) = 0.2

P(crawford components) = 0.5

P(defective | hall electronics) = 0.03

P(defective | schuler scales) = 0.05

P(defective | crawford components) = 0.05

P(defective) = P(defective | hall electronics) * P(hall electronics) + P(defective | schuler scales) * P(schuler scales) + P(defective | crawford components) * P(crawford components)

                     = 0.03 * 0.3 + 0.05 * 0.2 * 0.04 * 0.5

                     = 0.0092

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