# S4-3: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence.

Elaboration on this Achievement Objective

This means students will understand that probability is about the chance of outcomes occurring. At Level Four students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, for example the probability of someone being left-handed. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, for example different samples of 100 people will have different proportions. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Four students are expected to use systematic methods such as listing, tree or network diagrams with equally likely outcomes, and tables to find all the possible outcomes of simple one or two stage situations such as tossing two coins, drawing counters from a bag, or rolling two dice. Students should compare the distributions they get from trialling with the expectations obtained from models, accepting variation between samples and that the results of one sample do not impact on the next (independence), for example take samples of twenty counters, with replacement, from a bag that has one-half red, one-third blue and one-sixth yellow. Accept that an eight red, seven blue, and five yellow result is natural and that it will not be compensated by the next sample.