Question

A drawer contains 12 red socks and 8 black socks. Suppose that you choose 2 socks at random in the dark. What is the probability that you get a pair of red socks? *

Answer 1

34.74% probability that you get a pair of red socks.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the socks are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

Desired outcomes:

2 red socks, from a set of 12. So

`D = C_(12,2) = (12!)/(2!(12-2)!) = 66`

Total outcomes:

2 socks, from a set of 12+8 = 20. So

`T = C_(20,2) = (20!)/(2!(20-2)!) = 190`

What is the probability that you get a pair of red socks?

`p = (D)/(T) = (66)/(190) = 0.3474`

34.74% probability that you get a pair of red socks.