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

Let O shows the getting two odd numbers and S show the getting their sum as an even number.


Then ,



`P(O / S)=frac{P(O cap S)}{P(S)}`


`=frac{frac{5 C_{2}}{9 C_{2}}}{frac{(4 C_{2}+5 C_{2})}{9 {C_{2}}}}`

`=frac{5 C_{2}}{4 C_{2}+5 C_{2}}=frac{10}{16}=frac{5}{8}`