Elaboration on this Achievement Objective

This means students will understand that probability is about the chance of outcomes occurring. At Level Three students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, for example the chance of a day in March being fine. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, for example March 2008 is likely to be different from March 2009. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Three students are expected to use systematic methods such as listing, tree diagrams with equally likely outcomes, or tables to find all the possible outcomes of simple situations such as tossing coins, drawing cards, or rolling dice. They should accept that experimental samples from those situations, for example tossing a coin ten times, vary from one another, and from the proportions expected from a model, that is, most times five heads do not come up.