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NDA 2 2025 Maths, question 114

Topic: Probability

Q114

Out of 5050 consecutive natural numbers, two integers are chosen at random. What is the probability that their sum is odd?

  1. (a) 1/21/2
  2. (b) 24/4924/49
  3. (c) 1/41/4
  4. (d) 25/4925/49Correct answer

Solution.

Answer: (d) 25/4925/49

  1. Any 50 consecutive natural numbers contain 25 odd and 25 even numbers.
  2. An odd sum requires one of each, giving 25×25 favourable pairs out of C(50,2)=1225.
  3. Therefore the probability is 625/1225=25/49.