(4) 120 points] Suppose a warehouse is receiving \"Desk Lamps\" manufactured in

Question

(4) 120 points] Suppose a warehouse is receiving "Desk Lamps" manufactured in 3 different factories A, B, and C. Production share of factory A is 45% while the production shares for B and care 35% and 20% respectively. Suppose that 4% of lamps produced in factory A have defects, 2% produced by factory B have defects and 3% produced by factory C have defects. Assume that the warehouse manager selects one desk lamp at random for inspection. (a). What is the probability that the lamp selected is defective? (b). If the lamp selected is defective, what is the probability that it was produced by factory A? End

Explanation / Answer

P(factory A) = 0.45

P(factory B) = 0.35

P(factory C) = 0.2

P(defective | factory A) = 0.04

P(defective | factory B) = 0.02

P(defective | factory C) = 0.03

A) P(defective) = P(defective | factory A) * P(factory A) + P(defective | factory B) * P(factory B) + P(defective | factory C) * P(factory C)

= 0.04 * 0.45 + 0.02 * 0.35 + 0.03 * 0.2 = 0.031

B) P(factory A | defective) = 0.04 * 0.45 / 0.031 = 0.581

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