It is then useful to eliminate the denominator using the law of total probability.

The nomenclature used here parallels the phrase law of total probability.

The law of total probability can also be stated for conditional probabilities.

In the latter two examples the law of total probability is irrelevant, since only a single event (the condition) is given.

Applying the law of total probability, we have:

Lastly, using the law of total probability, the moment generating function can be given as follows:

This version of the law of total probability says that the expected value of this random variable is the same as Pr(A).

In probability theory, the 'law of total probability' is that "the prior probability of 'A' is equal to the prior expected value of the posterior probability of 'A'."

This finding violates the law of total probability, yet it can be explained as a quantum interference effect in a manner similar to the explanation for the results from double-slit experiment in quantum physics.

The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables.

In probability theory and mathematical statistics, the law of total cumulance is a generalization to cumulants of the law of total probability, the law of total expectation, and the law of total variance.

The law of total probability is the proposition that if 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 is measurable, then for any event of the same probability space: