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: \( 0 \le P(A) \le 1 \) 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: \( P(event)=\frac{number\ of\ favourable\ outcomes}{total\ number\ of\ outcomes} \)
  • calculate the probability of the complement of an event using the relationship \( P(an\ event\ does\ not\ occur)=1−P(the\ event\ does\ occur)=P( \overline{the\ event\ does\ occur})=P(event^c) \)
• 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 \( p \)