A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches drawer and pulls out 2 so

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14.Probability

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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

$\frac{4}{9}$

B

$\frac{5}{8}$

C

$\frac{5}{9}$

D

$\frac{7}{{12}}$

Solution

(a) Out of $9$ socks, $2$ can be drawn in ${}^9{C_2}$ ways.

Two socks drawn from the drawer will match if either both are brown of both are blue.

Therefore favourable number of cases is ${}^5{C_2} + {}^4{C_2}.$

Hence the required probability $ = \frac{{{}^5{C_2} + {}^4{C_2}}}{{{}^9{C_2}}} = \frac{4}{9}.$

Standard 11

Mathematics

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