Out of 50 consecutive natural numbers, two integers are chosen at...

Out of 50 consecutive natural numbers, there are exactly 25 even numbers and 25 odd numbers.

The total number of ways to choose two numbers from 50 is ^{50}C_{2}$.<br><br>The sum of two numbers is odd only when one number is even and the other is odd.<br><br>The number of ways to choose one even and one odd number is ^{25}C_{1} \times ^{25}C_{1}$.

The required probability is $\dfrac{^{25}C_{1} \times ^{25}C_{1}}{^{50}C_{2}}$.

$\dfrac{25 \times 25}{\dfrac{50 \times 49}{2}} = \dfrac{25 \times 25}{25 \times 49} = \dfrac{25}{49}$