Out of 50 consecutive natural numbers, two integers are chosen at random. What is the probability that their sum is odd?

Step-by-step solution

Out of 50 consecutive natural numbers, there are exactly 25 even numbers and 25 odd numbers. The total number of ways to choose two numbers from 50 is ⁵⁰C₂ . The sum of two numbers is odd only when one number is even and the other is odd. The number of ways to choose one even and one odd number is ²⁵C₁ ²⁵C₁ . The required probability is ²⁵C₁ ²⁵C₁ ⁵⁰C₂ . 25 25 50 49 2 = 25 25 25 49 = 25 49