Question

Two integers are selected at random from integers 1 through 11. If the sum is even, find the probability that both the numbers are odd. Select the correct answer from above options

Answer 1

Correct Answer - `3/5` Let A = event of choosing both odd numbers, B = event that sum of chosen numbers is even. In integers from 1 to 11, there are 5 even and 6 odd integers. `P(A)=(.^(6)C_(2))/(.^(11)C_(2))=3/11, P(B) =((.^(6)C_(2)+.^(5)C_(2))/(.^(11)C_(2)))=5/11, P(A nn B)= (.^(6)C_(2))/(.^(11)C_(2))=3/11`. `:.` required probability `=P(A//B)=(P(A nn B))/(P(B))`.