JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Probability

Two integers are selected at random from the set

{1, 2, \dots, 11}

. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:

Answer: (C)

Solution

The set has

5

even numbers and

6

odd numbers. The sum of two chosen numbers is even only when both are even or both are odd, so the favourable-for-conditioning count is

(2 5) + (2 6) = 10 + 15 = 25

. Of these, both are even in

(2 5) = 10

cases, so the conditional probability that both are even, given the sum is even, is

\frac{10}{25} = \frac{2}{5}

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option