CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability
Three suppliers X, Y and Z provide 50%, 30% and 20% of the components used by a Chennai firm. Their defective rates are 2%, 3% and 5% respectively. A component picked at random is found defective. What is the probability that it came from Supplier Z?
The probability is 10/29. The defective shares are 0.010 from X, 0.009 from Y and 0.010 from Z, totalling 0.029, so Z's share is 0.010 divided by 0.029, which simplifies to 10/29.
- A10/29Correct
- B9/29
- C10/19
- D20/29
Explanation
Joint probabilities: X 0.5×0.02 = 0.010, Y 0.3×0.03 = 0.009, Z 0.2×0.05 = 0.010. Total = 0.029. P(Z | defective) = 0.010/0.029 = 10/29. Option 10/19 wrongly omits Y's contribution... actually it uses 0.010/0.019.
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