Question

cards numbered from 1 through 31 are placed into a box and two cards are selected without replacement. Find the probability that both numbers selected are​ odd, given that their sum is even.

Find the probability that both numbers selected are​ odd, given that their sum is even.

Answer 1

Given that the sum of the 2 numbers is even, it is possible when either both the numbers are even or both are odd. Therefore number of ways to select 2 numbers such that the sum if even is computed as:

= Number of ways to select 2 even numbers + Number of ways to select 2 odd numbers

Probability that both numbers selected are odd given that the sum of two numbers is even is computed as:

= Number of ways to select two odd numbers / Total number of ways to get sum as even

Therefore 0.5333 is the required probability here.