Question

A drawer contains 7 red socks, 3 green socks, and 2 black socks. Two socks are chosen at random. What is the probability that they match? Express the answer in decimals.

Answer 1

P=0.38

Explanation:

We know that a drawer contains 7 red socks, 3 green socks, and 2 black socks. so, we have 12 socks.

We calculate the number of possible combinations to choose 2 socks out of 12.

`C_2^(12)=(12!)/(2!(12-2)!)=66`

We count the number of favorable combinations, that is, to choose from 7 red socks and choose 2, or to choose 2 from 3 green socks, or to choose 2 black socks.

`C_2^7+C_2^3+C_2^2=21+3+1=25`

So, the probability is

`P=(25)/(66)\\P=0.38`