Dressing In The Dark

Problem

Sally and Sara are dressing in the dark. They do that from time to time just for the fun of it. Mum has put out two red socks and two blue socks. Are the girls more likely to get a pair or one sock of each colour?

Teaching Sequence

1. Use the pairs of socks to introduce the problem. Hide the socks in a bag and get students to take turns selecting 2 socks from the bag of 4. After a number of attempts pose the problem.
2. Discuss their ideas following from the experiment.
   Do you think that it is more likely for the girls to get a pair? Why?
3. Brainstorm for ways to solve the problem (other than carrying out the experiment). Encourage the students to see that they need to find all the possible ways for the sock to be drawn from the bag.
4. As the students work on the problem in pairs or small groups ask them questions that focus on finding all the possible outcomes.
   How many different ways can you get socks from the bag?
   How do you know that you have found all the ways?
   If Sally pulls out a pair what happens to Sara?
5. Share solutions.

Extension to the problem

The next day there are 5 socks to choose from. There 3 blue socks and 2 red. Are the girls more likely to get odd socks or a pair?

Solution

Before we draw up the table we want to note that we’ll only worry about what Sally chooses. After all, if she chooses a pair, then so does Sara. And if Sally chooses a mixture, then so does Sara.

You will notice that in the table there are some blank spaces. This is because Sally can’t choose the first red sock (R1) and the first red sock (R1). She has to choose two different socks.

From the table there are 12 possibilities for Sally. We have indicated the pairs. There are only 4 possible pairs. This means that Sally is more likely to get an ‘odd’ pair than a proper pair.

Solution to the extension

There is even less chance of the girls getting a pair of socks here. This is because in the extension there are 20 ways of choosing the socks and there are only 8 pairs possible.