2: Plan

A detailed outline of how to run the simulation

In the playground example, each child will choose one of three activities at the park.

30% want to use the swings.

50% want to use the slide.

20% want to use the climbing net.

We need a way to simulate a group of six children visiting the park to play.

Tool

A tool uses a randomness generator to simulate outcomes for an individual event.

In this example, the tool simulates the choice of one child visiting the park. The chance of each outcome should match the playground description above.

I will use a random number generator on my calculator to generate a random number between 1 and 10, using IntRand#(1,10).

Three random numbers correspond to the swings because 3/10 = 30%.

I will colour the outcomes as shown to make it easier to keep track of which is which.

Note: Random outcomes could be generated using an Excel spreadsheet, calculator, or dice, depending on the conditions for your assessment.

Trial

A trial simulates the full situation once. It uses the tool repeatedly, until a stop condition is met.

In this example, the stop condition is a fixed count - every trial simulates six children visiting the park and choosing an activity.

A 'success' is an event we are trying to count. In this context, it is when there are three or more children who want to use the swings.

Each trial will consist of six tools (simulating six children visiting the park). Always stop after six tools.

Using the tool, I will record six random numbers, and colour them according to the activity.

I will also record whether the trial is a success, and how many children want to use the swings.

An example table showing two trials is below.

Note: A 'success' isn't always a good thing. Here, we're looking for trials in which some children want to use the swings but can't.

Table

The simulation will consist of repeating the trial a fixed number of times. The larger the number of trials, the better. (Why?)

How many trials is 'enough' will depend on the context, and the time constraints you are under.

In general, 50 trials is reasonable for finding an estimate of a probability. For an estimate of a mean, 30 trials may be enough.

Random variation will mean that every simulation is different. If you do another sample, you should not expect to get the same results, but they will (usually) be similar.

My simulation will consist of 50 trials, simulating 50 visits to the playground by a group of six children (and their activity choices). By doing 50 simulations, I should get a reasonable estimate of the probability that more than two children want to use the swings, and the mean number of children who want to use the swings.

How and why

Each part of the Tool & Trial section should describe how the situation is to be simulated, and WHY you have designed it this way.

It should also be in context, describing children and activities, not the numbers.

Scenario 2

Every night, Claire's cat Ebony goes outside hunting. From past experience, Claire knows that there is a 20% chance that Ebony will bring in an insect and 5% chance that she will bring in a lizard. On the other nights, Ebony does not bring in anything. Claire will keep Ebony inside at night for the rest of the week if Ebony ever brings in a lizard.

Claire wants to know how likely it is that Ebony will bring in three insects in one week.

Complete Worksheet 1 (below) on this scenario filling in the gaps and empty tables as required, then move on to Worksheet 2.

Do not complete run the simulation - just write about how it will work.

Sim Worksheet 1.pdf

Sim Worksheet 2.pdf

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