Product rule of probability

Product rule of probability applies to the coincidence of two events (A and B)([Error: Macro 'mathequation' doesn't exist] ).

In set theory symbols this is equivalent to the event C the intersection of events A and B:

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The following special cases can be distinguished.

Mutually independent events

Two sets of events are mutually independent if we have

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.

That is the probability of event B if A occurred is identical to the probability B without the occurrence of A.

For two mutually independent events the probabilities can be multiplied.

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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 independent events

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

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For not mutually independent events we can write:

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