Axioms of probability

Axioms of probability are the fundamental rules that define how probabilities should be calculated.

They provide a consistent framework for calculating probabilities of events and outcomes.

How to calculate

  1. The probability of any outcome in a sample space is a real number between 0 and 1, inclusive.

  2. The probability of the sample space is 1.

  3. If two events are mutually exclusive, then the probability that either event occurs is the sum of the probabilities of each event occurring.

  4. If two events are independent, then the probability of both events occurring is the product of the probabilities of each event occurring.

  5. The probability of the union of two events is the sum of the probabilities of each event minus the probability of the intersection of the two events.

Examples

  1. Axiom of Probability: Every outcome of an experiment has a probability between 0 and 1, inclusive. Example: When flipping a coin, the probability of getting heads is 0.5 and the probability of getting tails is also 0.5.

  2. Axiom of Additivity: The probability of the union of two disjoint events is equal to the sum of the probabilities of the individual events. Example: When rolling a fair 6-sided die, the probability of rolling a 4 or a 6 is 0.5 (0.33 + 0.167).

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