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} $