Q. 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) $\frac{10}{29}$
Explanation
(c)
The sum of the selected numbers is odd, if exactly one of them is even and one is odd.
$\therefore$ Favourable number of cases $= {\ ^{15}C}_{1} \bullet {\ ^{15}C}_{1}$
$\therefore$ Required probability $= \frac{{\ ^{15}C}_{1} \bullet {\ ^{15}C}_{1}}{{\ ^{30}C}_{2}} = \frac{15}{29}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.