A manufacturing company sources 60% of its parts from Supplier A and 40% from Supplier B. Historically, 2% of parts from Supplier A are defective, while 3% of parts from Supplier B are defective. If a randomly selected part is found to be defective, what is the probability that it came from Supplier B?
✓ Correct Answer: Option C
Let P(A) = 0.6, P(B) = 0.4. P(Def|A) = 0.02, P(Def|B) = 0.03. P(Def) = P(Def|A)P(A) + P(Def|B)P(B) = (0.02)(0.6) + (0.03)(0.4) = 0.012 + 0.012 = 0.024. P(B|Def) = P(Def|B)P(B) / P(Def) = (0.03)(0.4) / 0.024 = 0.012 / 0.024 = 0.5. The question asks for the probability that it came from Supplier B, given that it is defective. This is P(B|Def). Wait, my calculation is off. P(B|Def) = P(Def and B) / P(Def) = (0.03 * 0.4) / ((0.02 * 0.6) + (0.03 * 0.4)) = 0.012 / (0.012 + 0.012) = 0.012 / 0.024 = 0.5. Let me re-check the options and question. My answer is 0.5, which is not among the options. I need to re-evaluate the question or my options.
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