Question

A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. What is the probability that they match

• A. 4/9
• B. 5/8
• C. 5/9
• D. 7/12

Answer 1

Answer: (A)

4/9

Answer 2

Out of 9 socks, 2 can be drawn in ${ } ^ { 9 } \mathrm { C } _ { 2 }$ ways. Two socks drawn from the drawer will match if either both are brown of both are blue. Therefore favourable number of cases is ${ } ^ { 5 } \mathrm { C } _ { 2 } + { } ^ { 4 } \mathrm { C } _ { 2 }$ .

Hence the required probability = $\frac { { } ^ { 5 } \mathrm { C } _ { 2 } + { } ^ { 4 } \mathrm { C } _ { 2 } } { { } ^ { 9 } \mathrm { C } _ { 2 } } = \frac { 4 } { 9 }$