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Probability

infoWhy this? Probability provides a mathematical language for describing chance, fairness, and risk. Using probability scales, sample spaces, and complements develops logical reasoning and enables us to quantify uncertain events accurately.

scheduleWhy now? At the start of Year 7, this unit establishes shared language, notation, and the probability scale before these ideas are extended to experimental probability, combined events, and more structured representations in Years 8 and 9.

neurologyYou need to know

  • Probability is a measure of how likely an event is to occur, and is expressed as a number between 0 (impossible) and 1 (certain).
  • The probability scale can be described using words such as 'impossible', 'unlikely', 'even chance', 'likely', and 'certain'.
  • Probabilities can also be expressed as fractions, decimals, or percentages.
  • An experiment or trial is a process performed to produce an outcome.
  • An outcome is one possible result of an experiment or trial.
  • An event is a set of one or more outcomes.
  • The sample space is the set of all possible outcomes of an experiment or trial.
  • For a finite sample space of equally likely outcomes, the probability of an event is calculated as `\text{Probability of event} = \frac{\text{number of outcomes in the event}}{\text{total number of outcomes in the sample space}}`.
  • The sum of the probabilities of all outcomes in a sample space is 1.
  • The probability of an event not happening is equal to 1 minus the probability of the event happening.

rocket_launchYou must be able to

  • Use the probability scale to describe the likelihood of events, both with words and by placing events at the correct position on a 0 to 1 number line. Exemplification
  • List all possible outcomes for a given experiment or trial, such as rolling a die or flipping a coin. Exemplification
  • Decide whether the outcomes in a finite sample space are equally likely before calculating probability by counting outcomes, including in simple situations where outcomes are not equally likely.
  • Calculate the probability of a single event by counting the favourable outcomes and the total number of possible outcomes when all outcomes are equally likely. Exemplification
  • Calculate the probability of an event not happening, using the fact that probabilities sum to 1. Exemplification


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