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NDA 2 2025 Maths, question 109

Topic: Probability

Q109

An event XX can happen with probability pp and event YY can happen with probability qq. Further, XX and YY are independent events. Which of the following statements is/are correct?

I. The probability that exactly one of the events happens is p+q−pqp+q-pq.

II. The probability that at least one of the events happens is p+q−2pqp+q-2pq.

Select the answer using the code given below.

  1. (a) I only
  2. (b) II only
  3. (c) Both I and II
  4. (d) Neither I nor IICorrect answer

Solution.

Answer: (d) Neither I nor II

  1. Exactly one has probability p(1−q)+q(1−p)=p+q−2pq.
  2. At least one has probability 1−(1−p)(1−q)=p+q−pq.
  3. The two expressions in the statements have been interchanged, so neither is correct in general.