In a factory, machines A, B, and C produce 50%, 30%, and 20% of the total items respectively. Their defect rates are 1%, 5%, and 7%. If a randomly chosen item is defective, the probability it was produced by Machine A is:

In a factory, machines A, B, and C produce 50%, 30%, and 20% of the total items respectively. Their defect rates are 1%, 5%, and 7%. If a randomly chosen item is defective, the probability it was produced by Machine A is:

• A. 5/34
• B. 15/34
• C. 14/34
• D. 1/13

Answer: A) 5/34

Explanation: Total Defective Probability = (0.5×0.01) + (0.3×0.05) + (0.2×0.07) = 0.005 + 0.015 + 0.014 = 0.034. P(A|Defective) = 0.005 / 0.034 = 5/34.