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NDA 1 2025 Maths, question 111

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.

Q111

What is the probability that the bonus scheme will be introduced?

  1. (a) 17/45
  2. (b) 19/45
  3. (c) 23/45Correct answer
  4. (d) 26/45

Solution.

Answer: (c) 23/45

  1. By total probability: 310×49+12×29+45×13\frac{3}{10} \times \frac{4}{9} + \frac{1}{2} \times \frac{2}{9} + \frac{4}{5} \times \frac{1}{3}.
  2. =645+545+1245=2345= \frac{6}{45} + \frac{5}{45} + \frac{12}{45} = \frac{23}{45}.

Trap: The three appointment probabilities add up to 8/5, more than 1, so the data are inconsistent; the expected method is still this total-probability sum.