A drawer contains 5 brown socks and 4 blue so | vedclass

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(A) Total number of socks = $5 + 4 = 9$.The total number of ways to choose $2$ socks out of $9$ is given by ${}^9C_2 = \frac{9 	imes 8}{2 	imes 1} =

Vedclass · Accepted Answer

$\frac{4}{9}$

Vedclass · Answer

(A) Total number of socks = $5 + 4 = 9$.The total number of ways to choose $2$ socks out of $9$ is given by ${}^9C_2 = \frac{9 	imes 8}{2 	imes 1} = 36$.The socks will match if either both are brown or both are blue.Number of ways to choose $2$ brown socks from $5$ is ${}^5C_2 = \frac{5 	imes 4}{2 	imes 1} = 10$.Number of ways to choose $2$ blue socks from $4$ is ${}^4C_2 = \frac{4 	imes 3}{2 	imes 1} = 6$.Total favorable outcomes = $10 + 6 = 16$.Therefore,the required probability = $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{16}{36} = \frac{4}{9}$.

$A$ 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?

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