DR. NOR AZAH SAMATDepartment of MathematicsUniversiti Pendidikan
Sultan Idris
Representation of the Sample Space
Example 1.1: Draw the Venn and Tree diagrams for the experiment
of tossing a coin twice.
Venn DiagramTree Diagram
Example 1.2:
Probability of an event-given an experiment and sample space S,
the objective of probability is to assign to each event A a number
P(A), called the probability of the event A, which will give a
precise measure of the chance that A will occur.
-Probability: is a numerical measure of a likelihood that a
specific event will occur.
Basic properties of probability
1)For any event A, .
.
If is a finite or infinite sequence of mutually exclusive events
of S, then
Example 1.3:
An experiment has four possible outcomes: A, B, C, D, that are
mutually exclusive. Explain why the following assignments of
probabilities are not permissable.
P(A)=0.23, P(B)=0.46, P(C)=0.35, P(D)=0.10
P(A)=2/11, P(B)=6/11, P(C)=3/11, P(D)=1/11
Probabilities of individual outcomes
If A is an event in a discrete sample space S, then P(A) equals
the sum of the probabilities of the individual outcomes comprising
A.
Example 1.4If we flip a coin twice, what is the probability of
getting at most one head?
If an experiment can result in any one of N different equally
likely outcomes, and if n of these outcomes together constitute
event A, then the probability of event A:
Example 1.5: Find the probability of obtaining an even number in
one roll of a die.
