If two numbers are selected at random from the first 25 natural numbers, then the probability that their sum will be odd is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{13}{25}\)
Among 1, 2, …, 25 there are 13 odd numbers (1, 3, …, 25) and 12 even numbers (2, 4, …, 24).
The sum of two numbers is odd only when one is odd and the other is even:
\(\text{favourable selections} = 13 \times 12 = 156\)
Two different numbers can be selected in
\( \displaystyle ^{25}C_{2} = \frac{25 \times 24}{2} = 300 \text{ ways} \)
So
\( \displaystyle P(\text{sum odd}) = \frac{156}{300} = \frac{13}{25} \)