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Sum rule of probability

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Synonyms: Addition 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:

[Error: Macro 'mathequation' doesn't exist]

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.

[Error: Macro 'mathequation' doesn't exist]

For two mutually exclusive events the probabilities can be added.

[Error: Macro 'mathequation' doesn't exist]

Identical events

Two sets of events are identical if the intersection and union of these tow sets are identical.

[Error: Macro 'mathequation' doesn't exist]

For two identical events the probability is equal to each of the events.

[Error: Macro 'mathequation' doesn't exist]

Not mutually exclusive events

This is the general case from which all the special cases above can be deduces.

[Error: Macro 'mathequation' doesn't exist] [Error: Macro 'mathequation' doesn't exist]

For not mutually exclusive events we can write:

[Error: Macro 'mathequation' doesn't exist]

using the multiplication rule this can be transformed into

[Error: Macro 'mathequation' doesn't exist]

General rule

Generally the addition rule can be given for multiple events.

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More compactly written.

[Error: Macro 'mathequation' doesn't exist]

For proof of this rule see the wiki page.


Tags: Statistics


Categories: Mathematics

 
   

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