Question

A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is

• A. $\frac { 5 } { 108 }$
• B. $\frac { 18 } { 108 }$
• C. $\frac { 30 } { 108 }$
• D. $\frac { 48 } { 108 }$

Answer 1

Answer: (D)

$\frac { 48 } { 108 }$

Answer 2

Total socks $= 5 + 4 = 9$

The number of ways to select $2$ socks out of 9 = ${ } ^ { 9 } C _ { 2 }$

If number of ways to select both brown socks $= { } ^ { 5 } C _ { 2 }$

And number of ways to select both white socks $= { } ^ { 4 } C _ { 2 }$

$\therefore P$(Both brown or white) $= \frac { { } ^ { 5 } C _ { 2 } + { } ^ { 4 } C _ { 2 } } { { } ^ { 9 } C _ { 2 } } = \frac { 16 } { 36 } = \frac { 48 } { 108 }$.