Question

Socks in a drawer: In your sock drawer you have 4 blue, 5 gray, and 3 black socks. Half asleep one morning you grab 2 socks at random and put them on. Find the probability you end up wearing

(Round each answer to four decimal places if necessary.)

1. 2 blue socks.
2. no gray socks.
3. at least 1 black sock.
4. a green sock.
5. matching socks.

Answer 1

Here we have to find probability of selecting two socks from a drawer which contain 12 socks totally. Out of these 12, 4 are blue, 5 are gray and remaining 3 are black.

We can choose 2 out of these 12 using combination in 12C₂ ways.

but we have to remember another thing that these socks are of different colors. So from each color 2 socks can be selected in different ways using combinations. For example 2 blue socks can be selected in 4C₂ ways. So if we are finding the probability of selecting 2 blue socks, then we have to divide the 4C₂ by 12C₂ , since the actual number of cases of selecting 2 blue blub is 4C₂.

Now remaining answer is explained in the following pictures detailed,