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Standard Statistical analysis – Relative frequency and probability

This lesson comprises three (3) master classes focusing on:

  • Probabilities of simple events
  • Probabilities of compound events
  • Models and simulations of probability experiments

Content:

MS-S2


  • Review, understand and use the language associated with theoretical probability and relative frequency
    • construct a sample space for an experiment and use it to determine the number of outcomes
    • review probability as a measure of the ‘likely chance of occurrence’ of an event
    • review the probability scale: 0P(A)1 for each event A, with P(A)=0 if A is an impossibility and P(A)=1 if A is a certainty
  • Determine the probabilities associated with simple games and experiments
    • use the following definition of probability of an event where outcomes are equally likely: P(event)=number of favourable outcomestotal number of outcomes
    • calculate the probability of the complement of an event using the relationship P(an event does not occur)=1P(the event does occur)=P(¯the event does occur)=P(eventc)
  • Use arrays and tree diagrams to determine the outcomes and probabilities for multi-stage experiments
    • construct and use tree diagrams to establish the outcomes for a simple multi-stage event
    • use probability tree diagrams to solve problems involving two-stage events
  • Solve problems involving simulations or trials of experiments in a variety of contexts
    • perform simulations of experiments using technology
    • use relative frequency as an estimate of probability
    • recognise that an increasing number of trials produces relative frequencies that gradually become closer in value to the theoretical probability
    • identify factors that could complicate the simulation of real-world events
  • Solve problems involving probability and/or relative frequency in a variety of contexts
    • use existing known probabilities, or estimates based on relative frequencies to calculate expected frequency for a given sample or population, eg predicting, by calculation, the number of people of each blood type in a population given a two-way table of percentage breakdowns
    • calculate the expected frequency of an event occurring using np where n represents the number of times an experiment is repeated, and on each of those times the probability that the event occurs is p