Independent Events
==================

We define two events $A$ and $B$ to be independent in case:

.. math::
   \P(A\,B) = \P(A)\,\P(B)

and we often write $A\perp B$ to denote independent events.
   
The meaning of what the indepence of events means is when we look at
the conditional probability:

.. math::
   A\perp B \Longrightarrow \P(A\given B) = \P(A),

i.e. knowledge about $B$ does not influence the probability of $A$.
Evidently we also have $A\perp B\Longrightarrow\P(B\given A)=\P(B)$ .

A well known example is throwing with two dices. The outcome of the
first dice in no way influences the outcome of throwing with the
second dice. Therefore throwing 2 times 6 in a row is
$1/6\times 1/6 = 1/36$ .

An example of dependent events can be found in the previous section
about the marbles from the vases. The event ´Vase 1' and 'Red' are
evidently not independent.