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  4. 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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Q. 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 ?

Probability

Solution:

Total no. of possible out comes $= {^{9}C_2}$
Favourable outcomes = (1 Brown, 1 Brown) + (1 Blue, 1 Blue)
$\therefore $ P (favourable outcomes) $= {^5C_2 } + {^4C_2}$
$\therefore $ The reqd. probability
$ = \frac{^{5}C_{2} + ^{4}C_{2}}{^{9}C_{2}} = \frac{10+6}{36} = \frac{4}{9} $