**Remark**

For a noninductive argument for Proposition 4, note first that if a point of
the sample space is not a menber of any of the sets *E*_{i} then its probability
does not contribute anything to either side of the equality. On the other hand,
suppose that a point is in exactly *m* of the events *E*_{i}, where *m*>0. Then
since it is in
its probability is counted once in
;
also as this point is contained in
subsets of the type
,
its
probability is counted