Question

A student buys 2 pairs of socks at a time. He has a total of 6 pairs, 2 pairs (4 socks) of type A socks, 2 pairs of type B socks, and 2 pairs of type C socks. So he has 12 socks total, 4 of each type. The student stores the socks randomly in a basket. In the morning it is dark so the student cannot see what type of sock he is pulling from the basket. If he pulls 2 socks from the basket, what is the probability that they match?

Answer 1

Answer:

The probability is 0.2727

Step-by-step explanation:

There are nCk combinations or ways to take k elements from a group of n elements. So, nCk is calculated as:

$nCk=\frac{n!}{k!(n-k)!}$

Then, there are 66 ways to select two socks from the 12 that are in the basket. This is calculated as:

$12C2=\frac{12!}{2!(12-2)!}=66$

Additionally, if the student match the socks, he have 3 possibilities:

1. He match socks type A

2. He match socks type B

3. He match socks type C

There are 6 ways to match socks type A, 6 ways to match socks type B and   6 ways to match socks type C. This is calculated as:

$4C2=\frac{4!}{2!(4-2)!}=6$

Because the student should select 2 socks type A from the 4 socks type A that are in the basket and it is the same calculation for socks type B and Type C.

Finally, there are 18 possibilities to match the socks, so the probability is calculated as:

$P=\frac{6+6+6}{66}=\frac{18}{66}=0.2727$