Question

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

Answer 1

(c) 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 = $\frac{{}^{15}C_1\times {}^{15}C_1}{{}^{30}C_2}=\frac{15}{29}$