Question

Out of 30 consecutive numbers, 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

Answer: (C)

$\frac { 15 } { 29 }$

Answer 2

The total number of ways in which 2 integers can be chosen from the given 30 integers is ${ } ^ { 30 } C _ { 2 }$ The sum of the selected numbers is odd if exactly one of them is even and one is odd.

\ Favourable number of outcomes = ${ } ^ { 15 } C _ { 1 } \cdot { } ^ { 15 } C _ { 1 }$

$\therefore$ Required probability $= \frac { { } ^ { 15 } C _ { 1 } \cdot { } ^ { 15 } C _ { 1 } } { { } ^ { 30 } C _ { 2 } } = \frac { 15 } { 29 }$.