A bag contains 5 brown and 4 white socks. A man pulls out two socks. probability that these are of s

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14.Probability

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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

$\frac{{48}}{{108}}$

Solution

(d) 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}}$.

Standard 11

Mathematics

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