Sum rule of probability describes the probability of the combination of two events (A or B) (). In set theory symbols this is equivalent to the event C the union of events A and B:
The following special cases can be distinguished.
Mutually exclusive events
Two sets of events are mutually exclusive if the intersection between these two sets is empty.
For two mutually exclusive events the probabilities can be added.
Identical events
Two sets of events are identical if the intersection and union of these tow sets are identical.
For two identical events the probability is equal to each of the events.
Not mutually exclusive events
This is the general case from which all the special cases above can be deduces.
For not mutually exclusive events we can write:
using the multiplication rule this can be transformed into
General rule
Generally the addition rule can be given for multiple events.
More compactly written.
For proof of this rule see the wiki page.
Tags: Statistics
Categories: Mathematics
