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# Out of 30 Consecutive Integers, 2 Are Chosen at Random. the Probability that Their Sum is Odd, is (A) 14/29 (B) 16/29 (C) 15/29 (D) 10/29 - Mathematics

MCQ

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 =$\frac{^{15}{}{C}_1 \times ^{15}{}{C}_1}{^{30}{}{C}_2} = \frac{15}{29}$

Concept: Probability - Probability of 'Not', 'And' and 'Or' Events
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Q 24 | Page 72
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