**Proposition**

In other words, exactly one of the events must occur. By writing and using the fact that the events

Thus Equation (3.3) shows how, for given events
of which
one and only one must occur, we can compute *P*(*E*) by first conditioning on
which one of the *F*_{i} occurs. That is, Equation (3.3) states that *P*(*E*) is
equal to a weighted average of *P*(*E*|*F*_{i}), each term being weighted by the
probability of the event on which it is conditioned.

Suppose now that *E* has occurred and we are interested in determining which
one of the *F*_{j} also occurred. By Equation (3.3), we have the following
proposition.

**Proposition**