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

Options

A. `(2)/(5)`
B. `(1)/(2)`
C. `(7)/(10)`
D. `(3)/(5)`

Answer

A

Explanation

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)`