### Why use this problem

This problem will help students to understand the concept of a probability distribution: various results are possible, and each result occurs with a certain probable frequency. It will help students to understand that there is some structure in random processes, even though individual parts of the problem are random.

### Possible Approach

Cut out the 16 grids and ask students to work in pairs to group the numbers into four sets of four.

Once the students have grouped the pairs ask them to explain in turns to the rest of the group the reasoining behind their grouping. Encourage them to present their arguments as clearly as possible. Do the others agree or disagree? Can the others refine their argument?

Once the cards are sorted, can students suggest the probability distributions from which the cards were drawn? They can use the distribution maker interactivity to help.

### Key Questions

• Describe the cards in words.
• How might you start to quantify the data on each card more precisely? How would you represent this?
• Can you spot any patterns occurring in some of the cards? Does this help you to give a grouping?
• Can you know for sure that you have correctly grouped the cards? Can you think of any other sensible ways in which the cards may have been grouped?

### Possible Extension

Can you suggest possible distributions from which the numbers on each card were drawn? Can you suggest distributions from which the cards were unlikely or impossible to be drawn?

### Possible Support

Students struggling to start should be asked to make frequency and cumulative frequency tables. Can they spot any patterns in these? If your students are having trouble getting started, you might like to try the similar Stage 4 problem Which list is which?