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NDA 2 2025 Maths, question 107

Topic: Probability

Q107

A person XX speaks the truth 44 out of 55 times and person YY speaks the truth 55 out of 66 times. What is the probability that they will contradict each other in stating the fact?

  1. (a) 3/103/10Correct answer
  2. (b) 1/151/15
  3. (c) 1/61/6
  4. (d) 7/107/10

Solution.

Answer: (a) 3/103/10

  1. They contradict each other when exactly one of them tells the truth.
  2. P=45×16+15×56=430+530=930=310P = \frac{4}{5} \times \frac{1}{6} + \frac{1}{5} \times \frac{5}{6} = \frac{4}{30} + \frac{5}{30} = \frac{9}{30} = \frac{3}{10}.

Trap: This assumes the two speak independently about a yes-or-no fact, which is the standard reading.