Download Probability Definition: The probability of a given event is an

Probability
Definition :
The probability of a given event is an
expression of likelihood of occurrence of an
event .A probability is a number which
ranges from 0 to 1.
0 for an event which cannot occur
1 for an event which can occur
Importance for the concept of Probability
According to Ya-lun Chou :
“Statistics as a method of decisionmaking under uncertainty, is founded
on probability theory, since probability
is at once the language and the
measure of uncertainty and the risks
associated with it .”
Experiment :
The term experiment refers to processes
which result in different possible outcomes
or observations.
Random Experiment :
1) all possible outcomes are known in
advance.
2) none of the outcomes can be predicted
with certainty.
Note :
Each performance of a random experiment is
called a Trial and the result of a
performance ( or trial) is called an outcome
or case.
Sample Point :
The outcome of the random experiment is
called a sample point.
Sample space :
The set of all possible outcomes ( or sample
points) of a random experiment is called a
sample space.
Finite Sample space :
A sample space is said to be finite if it
contains a finite number of sample points.
Infinite Sample space :
A sample space is said to be infinite if it
contains a infinite number of sample points.
Discrete Sample space:
A sample space is said to be discrete if it
contains finite or finitely many or countably
infinite sample points which can be arranged into
a simple sequence E1,E2…….. Corresponding to
natural number.
Continuous Sample space :
A sample space is said to be continuous if it
contains non-denumerable(uncountable)
number of sample points.
Events:
A subset of a sample space is called an
event. An empty subset φ of S us called
impossible event and the space itself is
called a certain event.
The subset containing a simple sample point is
known as simple event or elementary event.
Types of event
Equally like Events :
Two or more events are said to be equally
likely if any one of them can not be expected to
occur in preference to the others.
Example:
In a tossing of an unbiased coin, Head
is likely to come up as tail.
Composite Event :
The union of two events A & B denoted by A U B
and A + B is called a composite event of A & B.
Compound Event:
The intersection of two events A & B denoted by A∩B
or AB is called compound event of A & B.
Mutually Exclusive ( or Incompatible) Events :
Two events are said to be mutually exclusive if they
have no sample point in common i.e. A∩B =Ф
Exhaustive events :
Two events are exhaustive if their union is equal to the
sample space.
Independent Events:
Two or more events are said to be independent if the
occurrence of one does not affect the occurrence of the
other.
Dependent Events :
Two events are said to be dependent if the
occurrence of one affects the occurrence of the
other.
Mutually exclusive & Exhaustive Events :
A number of events are said to be mutually
exclusive & exhaustive events if
i) every two of them are mutually exclusive
ii)one of them necessarily occurs in any trial.