Joint Probability

A joint probability is the likelihood of multiple events occurring, either simultaneously or sequentially. The joint probability of two events is notated as P(A ∩ B), or sometimes more informally as P(AB).

Contents

  1. Joint Probability
    1. Decomposition

Decomposition

The intersection of two events A and B is the same as event A times the conditional probability of B given A.

This can be expanded out to any number of events.

P(A1 ∩ A2 ∩ ... ∩ An-1 ∩ An) = P(A1|A2 ∩ ... ∩ An) ... P(An-1|An) P(An)

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