MAT Exam 2021 Paper

Concept:The sum of two integers is odd only when one integer is odd and the other is even.Explanation:Out of 20 consecutive positive integers, there are exactly 10 odd and 10 even integers.Total number of ways to choose 2 integers from 20 is:$\binom{20}{2} = 190$.Number of favourable ways to choose 1 odd and 1 even integer is:$10 \times 10 = 100$.Therefore, the required probability is:$\frac{100}{190} = \frac{10}{19}$.Answer:Option A: $\frac{10}{19}$.