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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