Question

• Work the following probability sock problem, keeping in mind that this is a problem without replacement. When you take out a sock, it stays out.

Sock Problem:

Your sock drawer is very unorganized. No socks are paired, and they are all just thrown randomly into the drawer. You do know that the drawer has four red socks and four blue socks in it. You want to get some socks to wear in the morning, but you do not want to turn on a light for fear of waking up your family.

• • If you draw two, what is the probability of a red pair match?
• • If you draw two, what is the probability of a match of any color?
• • If you draw three, what is the probability of a match of any color?
• • Describe your thinking and process.
• Include your thinking/reasoning on this problem, answers to the questions in fractional form (not decimals or percentages), and the specific thinking path that led you to the answers.

Answer 1

Drawer contains 4 red socks and 4 blue socks. The selection is without replacement.

P(red pair match)=4C2/8C2 =6/28 =0.214

We need to choose 2 out of 4 socks to get a red pair(4C2)

Total ways are to choose 2 socks out of 8 socks (8C2)

similarly P(any pair match) = 4C2+4C2/8C2 = 6+6/28 =0.428

We can have any color match(red or blue)

P(pair match when we draw three) =?

Total ways=8C3 as we choose 3 socks out of 8 socks for sample space.

For favourable cases, P(All three are red) + P( all three are blue) + P( 1 red,2 blue) +P( 2 red, 1 blue)

Total no. of favourable cases=4C3+4C3+4C1*4C2+4C1*4C2

Therefore required probability =4C3+4C3+4C1*4C2+4C1*4C2/8C3

= 4+4+4*6+4*6/56=56/56=1

Because we cannot choose three we always gets a pair of socks. Since we only have 2 colors.