Question

Two integers are selected at random from the set {1,2,…………..,11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is A. `(2)/(5)` B. `(1)/(2)` C. `(7)/(10)` D. `(3)/(5)` Select the correct answer from above options

Answer 1

Correct Answer - A In {1,2,3,……,11} there are 5 even numbers and 6 odd numbers . The sum even is possible only when both are odd or both are even . Let A be the event that denotes both numbers are even and B be the event that denotes sum of numbers is even . Then , `n(A)=""^(5)C_(2)+""^(6)C_(2)` . Required probability `P(A//B)=(P(A cap B))/(P(B)) =(""^(5)C_(2)//""^(11)C_(2))/(((""^(6)C_(2)+""^(5)C_(2)))/(""^(11)C_(2)))=(""^(5)C_(2))/(""^(6)C_(2)+""^(5)C_(2))=(10)/(15+10)=(2)/(5)`