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Question
Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is
Options
14/29
16/29
15/29
10/29
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Solution
15/29
The total number of ways in which two integers can be chosen from the given 30 integers is 30C2.
The sum of the selected numbers is odd if exactly one of them is even or odd.
∴ Favourable number of outcomes = 15C1 × 15C1
Hence, required probability =\[\frac{^{15}{}{C}_1 \times ^{15}{}{C}_1}{^{30}{}{C}_2} = \frac{15}{29}\]
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