Muokataan osiota sivusta Bayesin teoreema

==== Englanninkielisen Wikipedia-artikkelin ''Simple statement of theorem'' -osio ====
{{Malline:quotation|
Bayes gave a special case involving [http://en.wikipedia.org/wiki/Continuous_probability_distribution continuous] prior and posterior probability distributions and [http://en.wikipedia.org/wiki/Discrete_probability_distribution discrete probability distributions] of data, but in its simplest setting involving only discrete distributions, Bayes' theorem relates the [http://en.wikipedia.org/wiki/Conditional_probability conditional] and [http://en.wikipedia.org/wiki/Marginal_probability marginal] probabilities of events ''A'' and ''B'', where ''B'' has a non-vanishing probability:

:<math>P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}\,\! </math>.

Each term in Bayes' theorem has a conventional name:
* P(''A'') is the [http://en.wikipedia.org/wiki/Prior_probability prior probability] or [http://en.wikipedia.org/wiki/Marginal_probability marginal probability] of ''A''. It is "prior" in the sense that it does not take into account any information about&nbsp;''B''.
* P(''A''{{!}}''B'') is the [http://en.wikipedia.org/wiki/Conditional_probability conditional probability] of ''A'', given ''B''. It is also called the [http://en.wikipedia.org/wiki/Posterior_probability posterior probability] because it is derived from or depends upon the specified value of&nbsp;''B''.
* P(''B''{{!}}''A'') is the conditional probability of ''B'' given ''A''.
* P(''B'') is the prior or marginal probability of ''B'', and acts as a [http://en.wikipedia.org/wiki/Normalizing_constant normalizing constant]. 

Bayes' theorem in this form gives a mathematical representation of how the conditional probability of event ''A'' given ''B'' is related to the converse conditional probability of ''B'' given ''A''.}}