Question

Two numbers are selected at random from integers 1 through 9. If the sum is even, find the probability that both the numbers are odd. Select the correct answer from above options

Answer 1

Sum will be even if both the selected numbers are even or both the numbers are odd. Let `A = `Event that sum of two numbers is even. Here, we can select two numbers from `5` odd numbers or from `4` even numbers. `:. n(A) = C(5,2)+C(4,2) = 10+6 = 16.` Let `B = `Event that both numbers are odd. `:. n(B) = C(5,2) = 10` Also, `n(AnnB) = 10` `:.` Required probability , `P(B/A) = (n(AnnB) )/(n(A)) = 10/16= 5/8.`