**Proposition**

**Proposition**

*P*(*E*_{1}|*F*)=*P*(*E*_{1}|*E*_{2}*F*)*P*(*E*_{2}|*F*)+*P*(*E*_{1}|*E*_{2}^{c}*F*)*P*(*E*_{2}^{c}|*F*)

If we define
*Q*(*E*)=*P*(*E*|*F*), then *Q*(*E*) may be regarded as a probability
function on the events of *S*. Hence all of the propositions previously proved
for probabilities apply to it. For instance, we have