Two numbers are selected simultaneously from the set {6, 7, 8, 9, ……, 39}. If the sum of selected numbers is even then the probability that both the selected numbers are odd, is equal to

$\frac{40}{91}$

Total number of even numbers in the set is 18, and total number of odd numbers is 16.

A : Sum of selected numbers is even.

B : Selected numbers are odd.

$P(A)=\frac{{ }^{18} C_2+{ }^{16} C_2}{{ }^{34} C_2}, P(A \cap B)=\frac{{ }^{16} C_2}{{ }^{34} C_2}$

$P(B ~|~ A)=\frac{P(A \cap B)}{P(A)}=\frac{{ }^{16} C_2}{{ }^{16} C_2+{ }^{18} C_2}=\frac{40}{91}$