Problem 12E

A drawer contains 6 red socks, 4 green socks, and 2 black socks. Two socks are chosen at random. What is the probability that they match?

Solution :

Step 1 of 1:

We have red socks = 6

Green socks = 4 and

Black socks = 2

Our goal is :

We need to find the probability that the match.

Now we have to find the probability that the match.

The total number of socks is

=6+4+2

=12

Therefore the total number of socks is 12.

They are chosen randomly 2.

So the probability of red is

P(RedRed)=

P(RedRed)=

The probability of green is

P(GreenGreen)=

P(GreenGreen)=and

The probability of black is

P(BlackBlack)=

P(BlackBlack)=

Now we have to find the probability of sock match.

Then the probability of sock match is

P(sock match)=P(RedRed)+P(GreenGreen)+P(BlackBlack)

P(sock match)=++

P(sock match)=

P(sock match)=

P(sock match)=

P(sock match)=

Therefore the probability of sock match is .