Question

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. $\frac{2}{9}$
• B. $\frac{4}{9}$
• C. $\frac{5}{9}$
• D. $\frac{5}{8}$

Answer 1

Answer: (B)

$\frac{4}{9}$

Answer 2

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 $= \frac{^{5}C_{2} + ^{4}C_{2}}{^{9}C_{2}} = \frac{10+6}{36} = \frac{4}{9}$