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

(c) $\frac{15}{29}$

For sum of two integers to be odd, one integer should be even and the other should be odd.
In 30 consecutive integers, 15 are even and 15 are odd.

P(sum is odd) = P(first integer is odd and second is even) + P(first integer is even and second integer is odd)

$$\begin{gathered} =\frac{15}{30}\times \frac{15}{29}+\frac{15}{30}\times \frac{15}{29} \\ =\frac{450}{30\times 29} \\ =\frac{15}{29} \end{gathered}$$