Question

If out of 20 consecutive whole numbers two are chosen at random, then the probability that their sum is odd, is

• A. $\frac { 5 } { 19 }$
• B. $\frac { 10 } { 19 }$
• C. $\frac { 9 } { 19 }$
• D. None of these

Answer 1

Answer: (B)

$\frac { 10 } { 19 }$

Answer 2

The total number of ways in which 2 integers can be chosen from the given 20 integers ${ } ^ { 20 } C _ { 2 }$

The sum of the selected numbers is odd if exactly one of them is given and one is odd.

$\therefore$Favourable number of outcomes $= { } ^ { 10 } C _ { 1 } \times { } ^ { 10 } C _ { 1 }$

$\therefore$Required probability $= \frac { { } ^ { 10 } C _ { 1 } \times { } ^ { 10 } C _ { 1 } } { { } ^ { 20 } C _ { 2 } } = \frac { 10 } { 19 }$.