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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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.

Spinster Phenomenon

Spinster phenomenon is a behavior pattern among females that live in social compounds. When males are absent females take over the social roles of males.

Rational

Such a behavioral pattern as the spinster phenomenon evolved because it made evolutionary sense to maintain a group's social stability by a female that slips into the social role of a male. The converse is not of the same evolutionary importance as the female role makes no sense as long as there is no possibility to propagate. The only female function that can be seen readily adapted by pure male societies is giving sexual relief, which is by homosexuality observed in prison and military conditions[Error: Wrong macro arguments: "6747" for macro 'ref' (maybe wrong macro tag syntax?)] .

Examples

1. In a poultry farm, if there is no rooster, one hen adapts the rooster role. It even may try to copulate.
2. In human society after the male population was significantly reduced after two wars (WW1+2) in the 20th century feminism evolved. The human spinster phenomenon is a vivid example how biologically determined behavior patterns can become ideology when a pseudo-rational explanation is developed.

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