MathLiveLaw of total probability
Gives the probability of an event B by summing its conditional probabilities over a partition of the sample space into mutually exclusive events A_i that cover all outcomes, weighting each by the probability of that part. It is used when B is hard to compute directly but easy to analyse under each case.
P(B)=\sum_{i=1}^{n}P(B|A_{i})P(A_{i})What the symbols mean
| probability of event B | |
| events forming a partition of the sample space (mutually exclusive and exhaustive) | |
| number of events in the partition | |
| conditional probability of B given A_i | |
| probability of event A_i |
About this formula
- FieldMathematics
- TopicProbability theory
- LevelUniversity
- Also calledtotal probability formula, probability of an event over a partition, partition theorem, marginal probability from conditional probabilities, law of total probability for discrete events, formula
- SourceWikidata Q1989192
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