Question

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is

• A. $\frac{14}{29}$
• B. $\frac{16}{29}$
• C. $\frac{15}{29}$
• D. $\frac{10}{29}$

Answer 1

The correct option is C

$\frac{15}{29}$

The total number of ways in which two integers can be chosen from the given 30 integers is ${}^{30}{C}_2$.

The sum of the selected numbers is odd if exactly one of them is even or odd.

$\therefore$ Favourable number of outcomes

${=}^{15}{C}_1{\times }^{15}{C}_1$

Hence, required probability $=\frac{{}^{15}{C}_1{\times }^{15}{C}_1}{{}^{30}{C}_2}$

$=\frac{15}{29}$