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 ?

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) (2/9) (B) (4/9) (C) (5/9) (D) (5/8)

Tardigrade Admin · Accepted Answer

Total no. of possible out comes = 9C2 Favourable outcomes = (1 Brown, 1 Brown) + (1 Blue, 1 Blue) ∴ P (favourable outcomes) = 5C2 + 4C2 ∴ The reqd. probability = (5C2 + 4C2/9C2) = (10+6/36) = (4/9)

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 ?

$\frac{2}{9}$

$\frac{4}{9}$

$\frac{5}{9}$

$\frac{5}{8}$

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