Basic Concepts of Probability
A. Bourhim
Syracuse University
MAT121-Fall 2011
A. Bourhim (Syracuse University)
Basic Concepts of Probability
MAT121-Fall 2011
1 / 11

Rare Event Rule
If, under a given assumption, the probability of a particular observed event is
extremely small, we conclude that the assumption is probably not correct.
Definition
An
outcome
is the result of a single trial of an experiment.
An
event
is one or more outcomes of an experiment.
Any event which consists of a single outcome is called a
simple event
.
The
sample space
is the list of all outcomes.
Example
A single 6-sided die is rolled.
The possible outcomes of this experiment are: 1, 2, 3, 4, 5, 6.
Rolling a single number (like 1 or 2) is a simple event.
Rolling an even number is an event: 2, 4, 6.
Rolling an odd number is an event: 1, 3, 5.
Rolling a number large than 3 is an event: 4, 5, 6.
A. Bourhim (Syracuse University)
Basic Concepts of Probability
MAT121-Fall 2011
2 / 11

Notation
Events are denoted by
A
,
B
,
C
, ...
Probability is the measure of how likely an event
A
is, and is denoted by
P
(
A
)
.
Rule 1
: Relative Frequency Approximation of Probability
If an experiment is repeated
n
times and event
A
occurs
s
times, then the
relative frequency of
A
approximates
P
(
A
)
:
P
(
A
)
≈
s
n
.
Example
Suppose we toss a coin
50
times and have
27 heads
and
23 tails
. The relative
frequency of heads is:
27
50
=
54
%
.