A bag contains 5 brown and 4 white socks. If | vedclass

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(D) Let $A$ be the event of drawing $2$ brown socks and $B$ be the event of drawing $2$ white socks.Total number of ways to draw $2$ socks from $9$ is

Vedclass · Accepted Answer

$4/9$

Vedclass · Answer

(D) Let $A$ be the event of drawing $2$ brown socks and $B$ be the event of drawing $2$ white socks.Total number of ways to draw $2$ socks from $9$ is $^{9}C_{2} = \frac{9 	imes 8}{2 	imes 1} = 36$.Probability of drawing $2$ brown socks: $P(A) = \frac{^{5}C_{2}}{^{9}C_{2}} = \frac{10}{36} = \frac{5}{18}$.Probability of drawing $2$ white socks: $P(B) = \frac{^{4}C_{2}}{^{9}C_{2}} = \frac{6}{36} = \frac{3}{18}$.Since $A$ and $B$ are mutually exclusive events,the required probability is $P(A \cup B) = P(A) + P(B) = \frac{5}{18} + \frac{3}{18} = \frac{8}{18} = \frac{4}{9}$.

$A$ bag contains $5$ brown and $4$ white socks. If a man draws $2$ socks,what is the probability that they are of the same color?

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