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

Answer:

P=0.38

Step-by-step 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.

$C_2^{12}=\frac{12!}{2!(12-2)!}=66$

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

$P=\frac{25}{66}\\P=0.38$