Two numbers are selected at random from integers 1 to 9 . If their sum is even, what is the probability that both the numbers are odd?

Step-by-step solution

The set of integers is S = 1, 2, 3, 4, 5, 6, 7, 8, 9 . The number of odd integers is 5 (1, 3, 5, 7, 9) and the number of even integers is 4 (2, 4, 6, 8). The total number of ways to select two distinct numbers from 9 is ⁹C₂ = 9 8 2 = 36 . The sum of two numbers is even if both are odd or both are even. The number of ways to select two odd numbers is ⁵C₂ = 5 4 2 = 10 . The number of ways to select two even numbers is ⁴C₂ = 4 3 2 = 6 . The total number of ways to have an even sum is 10 + 6 = 16 . Let A be the event t