Question

In your drawer you have 10 white socks, 6 black socks, 4 brown socks and 2 blue socks. Your roommate is still asleep, and you cannot turn the light on while you get dressed. You reach in blindly and grab two socks. What is the probability of pulling out a matching pair of black socks?

Answer 1

Answer: Required probability is,

$\frac{36}{231}$

Step-by-step explanation:

Given,

White socks = 10,

Black socks = 6,

Brown socks = 4,

Blue socks = 2,

Total socks = 10 + 6 + 4 + 2 = 22,

Thus, the total ways of choosing any 2 socks = $^22C_2$,

Now, the ways of choosing a black socks = $^6C_1$

Thus, ways of choosing a pair of black socks = $^6C_1\times ^6C_1$

Hence, the probability of pulling out a matching pair of black socks

= $\frac{^6C_1\times ^6C_1}{^{22}c_2}$

= $\frac{36}{231}$