CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability
A factory in Pune has two machines. Machine A produces 60% of the items and Machine B produces 40%. If 5% of A's items and 10% of B's items are defective, what is the probability that an item chosen at random is defective?
The probability of a defective item is 0.07, found by weighting each machine's defect rate by its share of output: 0.6×0.05 plus 0.4×0.10 gives 0.03 plus 0.04, which equals 0.07.
- A0.07
- B0.08Correct
- C0.10
- D0.075
Explanation
Total probability: P(D) = 0.6×0.05 + 0.4×0.10 = 0.03 + 0.04 = 0.07. Check: 0.07 is the weighted average of 5% and 10%. Wait, 0.03+0.04 = 0.07, so the correct value is 0.07, not 0.08.
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