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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.
Solution:
Exercises 1.1:
(1)
(2)
(3)
Example 1.6:
Example 1.7:
Example 1.8:
Example 1.9:
Example 1.10:
Example 1.11:
Exercises 1.2:
(1)
(2)
(3)
Exercises 1.2 (continue):
(4)
Example 1.12:
Example 1.13:
Example 4.15:
Example 4.16:
Exercises 1.3:
(1)
(2)
Exercises 1.3 (continue):
(3)
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