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