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 a pair of red socks and a pair of blue socks. Are the girls more likely to get a pair or one sock of each colour?

What is this problem about?
This is a problem about drawing possibilities, making a systematic list, or using equipment to count all the possibilities. I’ll actually do it using a table. After that there is some comparing to do to see which occurs most often.

Achievement Objectives
Statistics (Level 3)
- use a systematic approach to count a set of possible outcomes
- predict the likelihood of outcomes on the basis of a set of observations

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (systematic list, draw a picture, use equipment).

Resources
A pair of red and blue socks to introduce the problem
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- Work systematically to identify all the possible outcomes.
- Describe events using everyday language.

1. Use the pairs of socks to introduce the problem. Hide the socks in a bag and get children 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 children to see that they need to find all the possible ways for the sock to be drawn from the bag.
4. As the children 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 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 highlighted the pairs. There are only 4 possible pairs. This means that Sally is more likely to get an ‘odd’ pair than a proper pair.