your sock drawer contains 6 blue socks, 8 black socks, and 10 white socks. What is the probability that you will randomly pick a pair of socks that mathc?

Question

your sock drawer contains 6 blue socks, 8 black socks, and 10 white socks.  What is the probability that you will randomly pick a pair of socks that match?

Answer 1

In this problem you are choosing items without replacement.

There are a total of 6 + 8 + 10 = 24 socks

The probability of choosing a blue sock initially is 6/24 = 1/4.

Given that the first sock chosen is blue, the probability of choosing another blue sock is 5/23, since there are 5 blue socks left in the drawer of 23 remaining socks. Thus the probability of choosing two blue socks is
(1/4)*(5/23) = 5/92.

A similar approach yields a probability of (8/24)*(7/23) = (1/3)*(7/23) = 7/69
of choosing 2 gray socks.

For 2 black socks we get (10/24)*(9/23) = (5/12)*(9/23) = 15/92.

The probability of picking 2 matching socks is the sum of 3 above results:

(5/92) + (7/69) + (15/92) = (15 + 28 + 45)/276 = 22/69.

Probability And Statistics Help

Answer 2

3/24