Two integers are selected at random from integers 1 through 11. If the sum is even, find the probability that both the numbers are odd.

Options

A. `(3)/(5)`
B. `(2)/(5)`
C. `(1)/(5)`
D. `(4)/(5)`

Answer

A

Explanation

Out of integers from 1 to 11, there are 5 even integers and 6 odd integers.
Consider the following events :
A= Both the numbers chosen are odd,
B=The sum of the numbers chosen is even.
`therefore` Required probability
`=P(A//B)`
=Probability that the two numbers chosen are odd if it is given that the sum of the sum of the numbers chosen is even.
`=(.^(5)C_(2))/(.^(5)C_(2)+.^(6)C_(2))=(3)/(5)`