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26.5 Chapter summary

  • Probability is a way of describing how likely an event is to occur.
  • An experiment is a test that we do to find out if something is true or to learn something. It is an uncertain process.
  • An outcome is a single result of an experiment.
  • The sample space (\(S\)) is the set of all possible outcomes of that experiment.
  • The size of the sample space (the total number of possible outcomes) is written as \(n(S)\).
  • An event (\(E\)) is a specific set of outcomes of an experiment that you are interested in.
  • The number of outcomes in the event is written as \(n(E)\).
  • An event that is described as “impossible” has a probability of \(0\).
  • An event that is described as “certain” has a probability of \(1\).
  • Probabilities can be expressed as decimal fractions between \(0\) and \(1\); or percentages between \(0 \%\) and \(100 \%\); or fractions between \(0\) and \(1\).
  • The probability of an event is the number of outcomes in the event set divided by the number of possible outcomes in the sample space: \(P(E) = \frac{n(E)}{n(S)}\).
  • Frequency is the number of times an event occurs.
  • Relative frequency is the observed number of outcomes for a certain number of trials.
  • Relative frequency \((f)\) is calculated by dividing the number of positive outcomes \((p)\) by the total number of trials \((t)\): \(f = \frac{p}{t}\)
  • As the number of trials increases, the relative frequency gets closer to the theoretical probability.