A factory has 3 machines producing 20%, 30%, and 50% of total output. Their defect rates are 2%, 3%,…
The probability of a defective item is (0.20 × 0.02) + (0.30 × 0.03) + (0.50 × 0.04) = 0.033. The probability that an item is both defective and from Machine 2 is 0.30 ×…
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A factory has 3 machines producing 20%, 30%, and 50% of total output. Their defect rates are 2%, 3%, and 4% respectively. A defective item is selected randomly. Probability that it came from Machine 2 is closest to:
Answer and explanation
Correct answer B
The probability of a defective item is (0.20 × 0.02) + (0.30 × 0.03) + (0.50 × 0.04) = 0.033. The probability that an item is both defective and from Machine 2 is 0.30 × 0.03 = 0.009. Bayes’ rule gives 0.009 ÷ 0.033 = 3/11 ≈ 0.2727, closest to 0.27.
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Telangana SET (TG SET)