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1.017/1.010 Class 5
Combinatorial Methods for Deriving Probabilities
Deriving Probabilities
The basic idea of the conceptual/deductive approach for deriving
probabilities is to break the composite experiment into parts (sub
experiments).
These parts are selected so that events for each part have
readily identified probabilities (e.g. they are equally likely).
The rules of
probability can then be used to derive the probability of complex events for
the composite experiment.
The approach is usually applied to problems with a finite number of
discrete outcomes.
The simplest application is an experiment that divides into a number of sub
experiments with
independent equally likely outcomes
.
In this case, suppose
A
is the event of interest and
S
is the sample space.
Then the probability of
A
is the ratio of the number of outcomes
N
(
A
) in
A
to the
total number of outcomes
N
(
S
)
:
)
(
)
(
)
(
S
N
A
N
A
P
=
Types of Experiments
To evaluate numbers of outcomes and probabilities we need to distinguish
different kinds of experiments:
Sampling with replacement
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 Spring '05
 GeorgeKocur

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