Question

Out of $40$ consecutive numbers two are chosen at random the probability that their sum is odd is......

• A. $\frac{20}{39}$
• B. $\frac{2}{7}$
• C. $\frac{25}{36}$
• D. $\frac{26}{36}$

Answer 1

The correct option is A $\frac{20}{39}$

To get the sum of $2$ integers as odd one must be even and the other one must be odd.

In $40$ consecutive integers, $20$ are even and $20$ are odd.

${}^{20}{C}_1$$=$ to select one odd number from $20$ numbers.

${}^{20}{C}_1$$=$ to select one even number from $20$ numbers.

${}^{40}{C}_2$$=$ to select two random numbers from $40$ numbers

Hence the probability that their sum is odd is $\frac{{}^{20}{C}_1{\times }^{20}{C}_1}{{}^{40}{C}_2}=\frac{20}{39}$