NDA 2025 · PYQ · Probability / Bayes Theorem · medium
The probabilities that A, B and C become managers are 3/10, 1/2 and 4/5 respectively. The probabilities that bonus scheme will be introduced if A, B and C become managers are 4/9, 2/9 and 1/3 respectively. If the bonus scheme has been introduced, then what is the probability that the manager appointed was B?
A.5/23✓ Correct
B.6/23
C.7/23
D.8/23
Explanation
Using Bayes' theorem: P(B|Bonus) = P(B)·P(Bonus|B) / P(Bonus). From the previous question, P(Bonus) = 23/45. P(B)·P(Bonus|B) = (1/2)(2/9) = 1/9 = 5/45. Therefore P(B|Bonus) = (5/45)/(23/45) = 5/23.
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