This integral is the total probability of all basis states occurring, so it must be 1 as before:

The probabilities of each route have to be calculated and summed to give the total probability.

According to the model, the total probability of the model is:

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

The events considered must be mutually exclusive and have total probability 1.

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

The total probability of making an error can be expressed in the form:

It expresses the total probability of an outcome which can be realized via several distinct events, hence the name.

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

The total probability of establishment (E) can be determined using this equation.