(4). 120 points] Suppose a warehouse is receiving \"Desk Lamps\" manufactured in
ID: 3043450 • Letter: #
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% wh C are 35% and 20% respectively. Suppose that 4% of lamps produced in factory A have 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. ile the production shares for B and defects, (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?Explanation / Answer
A) P(defective) = 0.45 * 0.04 + 0.35 * 0.02 + 0.2 * 0.03 = 0.031
b) P(produced by A | defective) = P(defective | produced by A) * P(produce by A)/P(defective)
= 0.04 * 0.45/0.031 = 0.58
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