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.