Law of total probability

In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events—hence the name.

The law of total probability is the proposition that if ${\displaystyle \left\{{B_{n}:n=1,2,3,\ldots }\right\}}$ is a finite or countably infinite partition of a sample space (in other words, a set of pairwise disjoint events whose union is the entire sample space) and each event ${\displaystyle B_{n}}$ is measurable, then for any event ${\displaystyle A}$ of the same probability space:

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