Out of 40 consecutive natural numbers, two are chosen at ran... | MATH - USE OF PERMUTATIONS AND COMBINATIONS IN PROBABILITY | SolveeIt | Solveeit

Today, August 18

Question

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

Answer

$\frac { 20 } { 39 }$

Explanation

Solution

Required probability $= \frac { { } ^ { 20 } C _ { 1 } \times { } ^ { 20 } C _ { 1 } } { { } ^ { 40 } C _ { 2 } } = \frac { 20 \times 20 \times 2 } { 40 \times 39 } = \frac { 20 } { 39 }$ .