The purpose of this activity is to engage students in solving a probability problem using both theoretical and experimental (modelling) methods.

The background knowledge and skills that need to be established before and/or during this activity are outlined in the diagram below:

Click to show example questions for each heading

This activity may be carried out with step by step guidance, or by allowing the student to follow their own method of solution. The approach should be chosen in sympathy with students' skills and depth of understanding.

At the local hockey grounds, there are four fields, with one of the four being brand new artificial turf. The allocation of fields to play on for the draw in a ten round competition is random.

How many games would a team expect to play on the new turf?

Use random numbers to set up a simulation of this problem. Comment on the results of your simulation.

### The arithmetic approach (show more)

- The student is able to run a probability simulation, and to calculate using a theoretical probability, to find an expected value.

### The conceptual approach (show more)

- The student is able to run a probability simulation, and to calculate using a theoretical probability, to find an expected value and to compare the results of the two methods.