Question

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is

• A. $\frac { 14 } { 15 }$
• B. $\frac { 11 } { 15 }$
• C. $\frac { 7 } { 15 }$
• D. $\frac { 4 } { 15 }$

Answer 1

Answer: (C)

$\frac { 7 } { 15 }$

Answer 2

Required probability

= Either the balls are red or the balls are black

$= \frac { { } ^ { 8 } C _ { 2 } } { { } ^ { 15 } C _ { 2 } } + \frac { { } ^ { 7 } C _ { 2 } } { { } ^ { 15 } C _ { 2 } } = \frac { 28 + 21 } { 105 }$ $= \frac { 49 } { 105 } = \frac { 7 } { 15 }$.