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NDA 1 2025 Maths, question 112

Topic: Probability

Passage · Q111 to Q112

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.

Q112

If the bonus scheme has been introduced, then what is the probability that the manager appointed was B?

  1. (a) 5/23Correct answer
  2. (b) 6/23
  3. (c) 7/23
  4. (d) 8/23

Solution.

Answer: (a) 5/23

  1. By Bayes' theorem: P(B∣bonus)=12×2923/45P(B \mid \text{bonus}) = \frac{\frac{1}{2} \times \frac{2}{9}}{23/45}.
  2. =5/4523/45=523= \frac{5/45}{23/45} = \frac{5}{23}.

Trap: It uses the total from question 111, so it carries the same inconsistency in the given appointment probabilities.