In a factory, machines A, B, and C produce 30%, 45%, and 25% of total output, with defect rates of 2%, 3%, and 4% respectively. If a randomly selected item is defective, the probability it was produced by machine B is approximately:
A. 0.30
B. 0.50
C. 0.43
D. 0.45
Answer: Option C
Solution (By JKSSB Mock Tests)
Using Bayes' theorem: P(B|Defective) = [P(Defective|B) × P(B)] / [Σ P(Defective|machine) × P(machine)] = (0.03×0.45) / (0.02×0.30 + 0.03×0.45 + 0.04×0.25) = 0.0135 / 0.0315 ≈ 0.4286 ≈ 0.43.
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