DEFINITIONS OF
PROBABILITY
CLASSICAL PROBABILITY, EMPIRICAL PROBABILITY
SUBJECTIVE PROBABILITY, AXIOMATIC PROBABILITY
02
, CLASSICAL PROBABILITY
As we have learned that an outcome is the result of single trial of a random experiment. Th
definition of probability assumes that all outcomes in a sample space are equally likely to o
what are equally likely outcomes?
Outcomes having equal chances of occurrence are called equally likely outcomes.
In some situations we can fairly assume that all outcomes of a random experiment are equa
occur. For example, in a coin tossing experiment, there are two possible outcomes head and
of fair coin we can assume that head is as likely to occur as tail
As another example, when a fair die is rolled, there are six possible outcomes (1, 2, 3, 4, 5, 6
outcome has same chances of occurring.
Suppose there are n distinct equally likely outcomes in a sample space S an
𝒎
them are favorable to an event A, then P(A) =
𝒏
Example
R.E: Roll a fair die A
Sample Space is:
S = {1, 2, 3, 4, 5, 6} ; n=6
A: getting an even number m
A = {2, 4, 6}; m=3
𝒎 𝟑 𝟏 n
P(A) = = = = 𝟎. 𝟓𝟎 = 𝟓𝟎% Amjad Ali
𝒏 𝟔 𝟐
PROBABILITY
CLASSICAL PROBABILITY, EMPIRICAL PROBABILITY
SUBJECTIVE PROBABILITY, AXIOMATIC PROBABILITY
02
, CLASSICAL PROBABILITY
As we have learned that an outcome is the result of single trial of a random experiment. Th
definition of probability assumes that all outcomes in a sample space are equally likely to o
what are equally likely outcomes?
Outcomes having equal chances of occurrence are called equally likely outcomes.
In some situations we can fairly assume that all outcomes of a random experiment are equa
occur. For example, in a coin tossing experiment, there are two possible outcomes head and
of fair coin we can assume that head is as likely to occur as tail
As another example, when a fair die is rolled, there are six possible outcomes (1, 2, 3, 4, 5, 6
outcome has same chances of occurring.
Suppose there are n distinct equally likely outcomes in a sample space S an
𝒎
them are favorable to an event A, then P(A) =
𝒏
Example
R.E: Roll a fair die A
Sample Space is:
S = {1, 2, 3, 4, 5, 6} ; n=6
A: getting an even number m
A = {2, 4, 6}; m=3
𝒎 𝟑 𝟏 n
P(A) = = = = 𝟎. 𝟓𝟎 = 𝟓𝟎% Amjad Ali
𝒏 𝟔 𝟐
