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91038: Investigate a situation involving elements of chance

Updated December 2016. This document has been updated in its entirety to address new issues that have arisen from moderation.

Students need to provide evidence of using the experimental probability process detailed in Explanatory Note 3 of the standard.


A situation involving elements of chance needs to be provided in the activity. Students need to pose a question to investigate the situation and could make a prediction for the situation.

The experimental situation could be:

  • one for which a theoretical model exists, for example throwing two or more dice.
  • one for which a theoretical model does not exist, for example throwing a basketball into a basketball hoop.

An experiment such as throwing a tetrahedral die 60 times and investigating the distribution of the four possible outcomes is not at the appropriate curriculum level.

If the question is about a ‘fair game’ the plan needs to include a description of the game and an explanation of what a ‘fair game’ is.

Plan and Data

The variable for the investigation needs to be clear. For example, the number of successful shots when shooting sets of three free throws.

Students need to define the set of possible outcomes which need to link to the question. For example, if the question is ‘I wonder what the chance is of getting an even total when I add two dice numbers together’, the possible outcomes would be an odd and an even total.

Assessors may give feedback to students about their plan before data collection occurs.


Appropriate displays include a table of the data which has been collected, a bar graph and a long run relative frequency graph. Students need to produce the experimental probability distribution as part of the evidence for selecting and using appropriate displays.


Identifying patterns in the data includes noticing any patterns occurring while the experiment is being performed, looking at the experimental results and commenting on the frequency and long run relative frequency.

Comparing theoretical and experimental distributions

If appropriate, students are likely to show higher levels of thinking by investigating and/or comparing the experimental and theoretical distributions.


The conclusion needs to include an answer to the posed question.

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