# Probability: Level 5

The key idea of probability at level 5 is estimating probabilities and probability distributions from experiments and deriving probabilities and probability distributions from theoretical models for two- and three-stage chance situations and recognising the connections between experimental estimates, theoretical model probabilities and true probabilities.

At level 5 students are exploring two- and three-stage chance situations, for example using spinners, drawing marbles out of a bag (with replacement) tossing three dice, or rock, scissors and paper.  More complex chance situations can be explored, for example two spinners with different colour combinations on them, or two bags of marbles with different numbers of each colour in them, or a mixture such as a bag of marbles and a spinner.  Problems include ones like “Is the game fair?”

Students are systematically listing all possible outcomes using tree diagrams and other relevant tools such as two way tables.  Students are recording their results and plotting frequencies of outcomes.  Students are aware that in some chance situations outcomes are not equally likely.

Students are where possible comparing experimental estimates with theoretical model probabilities.  Students need to recognise that theoretical model probabilities and experimental estimates of probabilities are approximations of the true probabilities which are never known.  All probabilities lie in the range 0-1.

The three different types of chance situations described in level three need to be reinforced at this and other levels.

Link to statistical investigations: Students are exploring outcomes for two categorical variables in statistical investigations from a probabilistic perspective.

This key idea develops from the key idea of probability at level 4 where students are estimating probabilities and probability distributions from experiments and deriving probabilities and probability distributions from theoretical models for two-stage chance situations.

This key idea is extended in the key idea of probability at level 6 where students are exploring chance situations involving discrete random variables.