Database Reference
In-Depth Information
this question is determined by dividing the number of red balls in the urn by
the total number of balls in the urn, written as,
Probabilities always sum to 1, so it is also possible to answer “What is the
probability thatthenextball
won't
bered?”intermsoftheprobability ofthe
opposite event. For example,
Similarly, combinations of events can also be written the same way. The
probability of removing a red ball
or
a white ball is written,
This is the same as writing P(ball=red) + P(ball=white). In fact, so long as
the events are mutually exclusive, they can always be added in this way.
Things get a little bit more complicated when dealing with “and” events,
such as, “What is the probability that a red ball is removed from the urn
and then a white ball is removed from the urn?” In general, the probability
of these events will multiply rather than add. So, to answer the question,
you need both the probability of a red ball being drawn and the probability
of the white ball being drawn. The probability that the red ball has been
removed stays the same. However, the probability that a white ball is drawn
next depends on what happened with the red ball.
A
conditional probability
, written P(A|B), describes the relationship
between the first event and the second event. It is read as, “The probability
that A happens, given that B has already happened.” This allows the
previously mentioned “and” event to be decomposed into something more
tractable:
