CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability
A Chennai firm buys components from three suppliers X, Y and Z, who provide 50%, 30% and 20% of the supply, with defective rates of 2%, 3% and 5% respectively. A component chosen at random is defective. What is the probability that it was supplied by Z?
The probability is 10/29. The joint probabilities of a defective part are 0.010 from X, 0.009 from Y and 0.010 from Z, totalling 0.029. Z's share of this total is 0.010/0.029 = 10/29, which is the posterior probability under Bayes' theorem.
- A10/29Correct
- B9/29
- C1/5
- D5/29
Explanation
Joint probabilities: X = 0.5 x 0.02 = 0.010, Y = 0.3 x 0.03 = 0.009, Z = 0.2 x 0.05 = 0.010. Total = 0.029. P(Z | defective) = 0.010/0.029 = 10/29. The option 9/29 is Y's posterior, and 1/5 is Z's prior share ignoring defect rates.
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