Two integers are selected at random from the set . Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: A
Solution
From {1,2,...,11}: 5 even numbers {2,4,6,8,10} and 6 odd numbers {1,3,5,7,9,11}.
Sum is even when both are even or both are odd.
- Both even: C(5,2) = 10
- Both odd: C(6,2) = 15
- Total with even sum: 25
P(both even | even sum) = 10/25 = 2/5.
Sum is even when both are even or both are odd.
- Both even: C(5,2) = 10
- Both odd: C(6,2) = 15
- Total with even sum: 25
P(both even | even sum) = 10/25 = 2/5.
[JEE Main 2019 · 11 Jan · Shift I]