Conditional Probability of a Defective Component
A company manufactures a certain component in three factories: A, B, and C. Factory A produces 50% of the components and has a defect rate of 2%. Factory B produces 30% of the components and has a defect rate of 3%. Factory C produces 20% of the components and has a defect rate of 5%. If a component is selected at random and found to be defective, what is the probability that it was produced in Factory C?
A
0.33
B
0.40
C
0.05
D
0.20
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