Sum rule of probability

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.