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Chapter 5 – Probability
Defn
:
A random experiment
is one for which the outcome cannot be predicted with certainty.
Defn
:
The set of all possible outcomes of a random experiment is called the sample space
of the
experiment.
Defn
:
An event
is a subset of the sample space.
It may consist of one or more possible outcomes of
the experiment.
If the result of performing the experiment is an outcome contained in an event A, we
say that the event A has occurred.
Example
:
Let our random experiment consist of tossing a coin twice.
The sample space, S, consists of
the four possible outcomes.
S = {HH, HT, TH, TT}.
One event that we can define for this
experiment is the event that at least one Head results from tossing the coin twice.
This event may be
denoted by A = {HH, HT, TH}.
If we perform the experiment and the actual result is {HT}, then we
will say that the event A has occurred.
Defn
:
An event which contains a single outcome is called a simple event
.
An event which contains
more than one outcome is called a compound event
.
In the example above, A = {HH, HT, TH} is a compound event;
B = {HT} is a simple event.
The
probability
of an event is a number which measures the likelihood that the event will happen when
we perform the random experiment
.
How do we assign numerical probabilities to events?
There are three approaches to assigning probabilities to events when examining the outcome of a
random experiment:
1)
Classical method
:
In the classical approach, we assume that every outcome of the experiment is
equally likely.
If there are N possible outcomes of the experiment, then the probability of occurrence
of any one of those outcomes is 1/N.
In general, if E is an event which contains n(E) of the possible outcomes of a random experiment, and
if the total number of possible outcomes is n(S), the size of the sample space, then we say that the
probability of occurrence of the event E is
)
(
)
(
)
(
S
n
E
n
E
P
=
.
If we flip a fair coin twice, there are four possible outcomes, and we assign a probability of ¼ to each
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This note was uploaded on 07/28/2011 for the course STA 2014 taught by Professor Staff during the Fall '10 term at University of Florida.
 Fall '10
 Staff
 Statistics, Probability

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