Students who need a greater challenge, can find probabilities for three- and four-step experiments. For example 'What is the probability of rolling a 3 and 4 after two rolls of a dice?' is asking something different to 'When a dice is rolled twice, what is the probability of rolling a 3 followed by a 4?' They should also understand that ordered outcomes increases the amount in the sample space and therefore probability values will be affected. Whilst the order does not always matter, it is important for students to understand that this will depend on the wording of the question. For example when rolling a die, they may think the outcomes (3, 4) and (4, 3) are the same. For example, 'at least one' means one or more and 'less than five' does not include the value 5 etc.Ī common misunderstanding is that students think that the order of events doesn’t matter. Creating a glossary of specific mathematical terms used in probability may be useful to help students use correct terminology. For example, selecting two marbles from a bag containing 3 red marbles and 5 green marbles with and without replacement, to highlight the difference in probability values for the outcome of two red marbles.Įncourage students to read questions carefully and to highlight important terms.

To help students understand the concepts of with and without replacement, show an example to compare probabilities of a particular event. They can then find the corresponding probabilities for each event. Students conduct two-step chance experiments with and without replacement and record the results.Įncourage students to use tree diagrams or arrays to show the outcomes of a two-step experiment.

using tree diagrams, tables, simulations and technology).

At this level, students will explore different ways of displaying probability outcomes and calculating probabilities for events (E.g.

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