   Evolution is progress—
progress is creativity.  # Product rule of probability

Synonyms: Multiplication 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:

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

The following special cases can be distinguished.

## Mutually independent events

Two sets of events are mutually independent if we have

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

.

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.

[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 independent events

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

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

For not mutually independent events we can write:

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

Tags: Statistics

Categories: Mathematics

(c) Mato Nagel, Weißwasser 2004-2023, Disclaimer