Out of 50 consecutive natural numbers, two integers are chosen at random. What is the probability that their sum is odd?

Explanation

In 50 consecutive natural numbers, there are exactly 25 odd and 25 even numbers. The sum of two integers is odd if and only if one is odd and the other is even. The probability of choosing one odd and one even is \frac{\binom{25}{1} \times \binom{25}{1}}{\binom{50}{2}} = \frac{625}{1225} = \frac{25}{49}.

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