The Laplace Probability

Recap: Random Events

• a collection of outcomes of a random trial is called (random) event.
• Events are subsets of the sample space \(\Omega\)

Laplace experiments

• In a finitely sample space \(\Omega\) with finitely many outcomes {\(\omega_1,...,\omega_n\)}
• A Laplace experiment is a random experiment in which all possible outcomes have the same probability.
• Examples:
  • Tossing a coin: \(\Omega =\) {Head, Tail}. probability: \(\frac{1}{2}\)

Laplace probability

• Calculate the probability \(P(A)\) of an event \(A \subseteq \Omega\) as:
• \(P(A) = \frac{\text{number of outcomes for which event A occurs}}{\text{number of all possible outcomes}} = \frac{|A|}{|\Omega|}\)

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