The key idea of probability at level 4 is estimating probabilities and probability distributions from experiments and deriving probabilities and probability distributions from theoretical models for two-stage chance situations.

At level 4 students are experimenting with two-stage chance situations, for example tossing two coins, dice, pigs, drawing pins, a coin and a die. Students are systematically listing all possible outcomes including using tools such as two way tables. Students are recording their results and plotting frequencies of outcomes. Students are recognising that in some chance situations outcomes are not equally likely, for example getting two heads or a head and a tail.

Students are comparing their experimental results with others in the class. They should also where possible compare estimated probabilities and probability distributions from experiments with theoretical model probabilities and probability distributions.

Starting with a one-stage chance situation (e.g., tossing one coin) students need to recognise that estimates of probabilities from experiments should be based on a very large number of trials. Technology is a useful tool for large numbers of trials.

In addition students should be exploring the idea of independence in probability using a one-stage chance situation, for example tossing one coin or one pig. In this setting independence refers to sequences of trials where the outcome of one trial has no impact on the next trial. For example, five tosses of a fair coin have come up HHHHH, the probability of getting a head on the next toss is still ½.

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 simple categorical variables in statistical investigations from a probabilistic perspective. For example, using gender and tongue roll or not, what is the probability that a randomly selected student is a boy and can roll his tongue?

This key idea develops from the key idea of probability at level 3 where students are quantifying one-stage chance situations by deriving probabilities and probability distributions from theoretical models and/or estimating probabilities and probability distributions from experiments.

This key idea is extended in the key idea of probability at level 5 where students are 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.

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