In a bolt factory, machines A, B, C manufacture 20%, 30%, 50% of the bolts respectively, w…

Question

In a bolt factory, machines A, B, C manufacture 20\%, 30\%, 50\% of the bolts respectively, with defective rates 3\%, 4\%, 2\%. A bolt drawn at random is found defective; the probability it is from machine C is:

Accepted Answer

$$P(C\mid\text{Def}) = \frac{0.5\times0.02}{0.2\times0.03+0.3\times0.04+0.5\times0.02} = \frac{0.01}{0.028}=\frac{10}{28}=\frac{5}{14}$$

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