Nomenclature in probability theory is not wholly standard.
Sometimes the phrase law of total probability refers to the proposition that if { Bn : n = 1, 2, 3, ... } is a finite or countably infinite partition of a probability space and each set Bn is measurable, then for any event A we have
The phrase law of total probability is also used to refer to the proposition that says that under similar assumptions, we have
- The prior probability of A is equal to the prior expected value of the posterior probability of A.