Q. Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is
A) $\frac{14}{29}$
B) $\frac{20}{39}$
C) $\frac{1}{2}$
D) None of these
Explanation
(b)
The sum of two numbers is odd only when one is odd and other is even.
$\therefore$ Required probability$= \frac{\ ^{20}C_{1}.\ ^{20}C_{1}}{\ ^{40}C_{2}}$
$= \frac{20 \times 20}{\frac{40 \times 39}{2 \times 1}} = \frac{20 \times 20}{20 \times 39}$
$= \frac{20}{39}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.