In your drawer you have 10 white socks, 6 black socks, 4 red socks, and 2 purple socks. Your roommate is still sleep, and you can’t turn the light on while you are getting dressed. You reach in blindly and grab two socks. What is the probability of pulling out a matching pair of purple socks?

The required probability  is .

Step-by-step explanation:

Probability:

The ratio of the number of favorable outcomes to the number of possible outcomes.

Multiplication Rule:

P(A and B)= P(A ∩ B)= P(A)×P(B|A) =P(B)×P(A|B)

Addition Rule for disjoint events :

P(A or B) =P(A∪B)=P(A)+P(B)

Given, 10 white socks (W), 6 black socks (B), 4 red socks (R) and 2 purple socks (P).

Total number of socks =(10+6+4+2)=22

Probability of getting a purple sock on first drawn

=P(P₁)

After one purple socks is drawn,

The number of purple socks is =(2-1) =1

Total number of socks= (22-1)=21

Probability of getting a purple sock on second drawn

=P(P₂|P₁)

The probability of polling matching pair of purple socks is

=P(P₁)×P(P₂|P₁)

8/18 * 9/20

divide 8/18 by 2 on the top and bottom

4/9

4/9 * 9/20

4/20 * 9/9

4/20  

divide the top and bottom by 4

1/5