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.

Explanation

We know that,`5` are even and `6` are odd

Let,

`A=` Both numbers are odd

`B=` Sum of chosen numbers is even


From odd numbers, `2` numbers are chosen in `C_2^6` ways

For sum to be even, the `2` numbers are either even or odd.


`2` numbers are chosen such that sum is even in `C_2^6+C_2^5` ways

`P(A)=frac{C_2^6}{C_2^11}, P(B)=frac{C_2^6+C_2^5}{C_2^11}`

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