Question

Out of $40$ consecutive natural numbers, two are chosen at random. Probability that the sum of the number is odd, is

• A. $\frac{14}{29}$
• B. $\frac{20}{39}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

Answer: (B)

In out of $40$ consecutive numbers, $20$ are odd and $20$ are even numbers. Now, the sum of two numbers is odd only when one is odd and other is even.
$\therefore$ Required probability $=\frac{{}^{20}{C}_1{\cdot }^{20}{C}_1}{{}^{40}{C}_2}$
$=\frac{20\times 20}{\frac{40\times 39}{2\times 1}}=\frac{20\times 20}{20\times 39}$
$=\frac{20}{39}$