Running the simulation and estimating the probability

Running the trials

• Generate the random numbers, read them in groups the size of one trial, and record the result of each trial in a table or tally.
• Keep going until you have reached your planned number of trials — decided in advance, not when the answer starts looking convenient.
• Record every trial as you go, including the ones that produce a boring result. Recording is a named component of the process, and the marker needs to see the raw record, not just the total.
• Do not change the rules part-way through. If you realise the design is wrong, start again and say so in your report — a set of trials run under two different rules estimates nothing.

Describing the distribution of results

• Plotting how often each result happened gives the distribution of the outcome — a bar graph or dot plot.

• The standard asks you to select and use appropriate displays and measures, so the distribution needs describing, not just drawing. Cover:
  • Centre — the most common result, and the mean or median number of successes
  • Spread — the range of results that actually occurred
  • Shape — is it symmetric, or does it lean to one side?
  • Unusual features — results that almost never happened, or gaps
• Read the picture in context. Here, most trials of 5 shots give 3 or 4 makes, 0 makes almost never happens, and the distribution leans slightly toward the higher numbers — which is what you would expect from a player who makes most of their shots.
• The distribution answers questions the single estimate cannot, such as how unusual a bad night would be, and it is what turns a number into an interpretation.

Estimating the probability

• The estimate is the relative frequency — how often the event happened out of all trials:

$$\text{estimated probability} = \dfrac{\text{number of trials with the event}}{\text{total number of trials}}$$

• Count the trials where the event occurred, divide by the total, and state the estimate (as a fraction, decimal or percentage), in context.
• The answer is an estimate, and the wording must say so. "Based on 200 trials, the estimated probability is about 0.53" is right; "the probability is 0.53" claims more than a simulation can deliver.
• A different set of trials would give a slightly different answer. That variation is not a flaw in your work — it is the reason the next page is about how many trials to run.