Question

Situation: It is a cold, dark, and stormy winter morning. Your boss has called a 5
a.m. meeting before she leaves to catch a flight to the Bahamas for her vacation, and there is a power
outage. Your alarm does not go off and you sit up in bed with a fright at what you guess is about 4:45
a.m. You are trying frantically to get dressed and you need to reach into your sock drawer to get two
matching socks in the dark. Naturally, your mind wanders to solving probability equations. Your sock
drawer contains 20 total socks which consist of 10 matched pairs of socks. All of them are only black or
white and they are loose, disorganized randomly, and not bound together. This means you have 10 black
socks and 10 white socks in your disorganized drawer. You do not have a light source because your
phone did not charge and you cannot find a flashlight or a candle. You are completely in the dark! You
have to get dressed and go! You have to math fast!

1. Think for a minute and describe your optimal strategy for solving this problem in 50 words or
less.
2. Let’s say for a moment that all 20 socks are different colors meaning that none match. What is
the total number of different ways they could be combined in pairs?

3. Now consider all the socks are only black and white. What is the total number of different ways
they could be combined in pairs? (Suggestion: You might consider listing the sample space of all
possible outcomes.)

Answer 1