Question

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:

• A. $\frac{8}{33}$
• B. $\frac{40}{91}$
• C. $\frac{51}{91}$
• D. $\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2}$

Required probability
$=\frac{p\left(bothodd\right)}{p\left(sumeven\right)}=\frac{{}^{17}{C}_2}{{}^{17}{C}_2{+}^{17}{C}_2}=\frac{1}{2}$