Level Five

This means that students will calculate probabilities for probability situations that involve two or more events.  These events may be independent (for example rolling two dice, or tossing two coins) or dependent (for example drawing two cards from a deck of cards without replacement, or choosing to students from the class at random).  They will be able to model these situations using models such as tree diagrams, tables and systematic lists and assign theoretical probabilities as proportions using fractions, percentages and ratios, for example the odds of winning the game are 2:3.

Students at Level Five understand that elements of chance have an effect on the certainty of results from surveys or experiments. Through examples from real life they should understand that statistics usually involves situations where the actual probabilities are not known, for example, probability of catching a disease. They should recognise situations where deterministic theoretical models are not possible, for example chance of a bus being early, and distinguish them from situations where probabilities can be reasoned from all the possibilities.

This means that students will evaluate the statistical investigation or probability activity undertaken by others by considering features of the investigation. These features include the appropriateness of sampling methods (for example number, representativeness), quality of the data collection (for example questions asked, accuracy of measurement, fairness of the experiment), choices of measures (types of questions, and responses allowed), data analysis (technology use, choice of displays) and the extent to which claims made are supported by the evidence.