Probability TUTORIAL.pdf - CHAPTER 1: PROBABILITY 1.1...

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CHAPTER 1: PROBABILITY
1.1 Probability
- express the degree of uncertainty. The value ranges between 0 and 1.
0 ------------------------------------- 1
impossibility certainty
Some terminology
1. Experiment - is the process by which an observation is made.
2. Outcomes - the results from the experiment
3. Sample Space - the set which consisting of all possible outcomes, denoted by
S .
4. Event - is a subset of the outcomes set
Examples:
Experiment Outcomes Sample
Space
Event
Toss a coin Head, Tail S = {Head, Tail} A = getting a head
A= {head}
Roll a die
once
1, 2, 3, 4, 5, 6 S = {1, 2, 3, 4, 5,6 } B = getting odd
numbers
B = {1, 3, 5}
Toss a coin
twice
HH, HT, TH, TT S = { HH, HT, TH,
TT}
C = getting at least
one head
C = {HH, HT, TH}
Take a test Pass, Fail S = { Pass, Fail} D = fail the exams
D = {fail}
Select a
student
Male, Female S = {Male, Female} E = a female student
E = {female}
Chioce of
handset
HTC,Samsung,
iphone
S={HTC, Samsung,
iphone}
F = buying a HTC
F = {HTC}

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1.2 Basic Concepts of Probability
Let A be any event defined over S
1. 0  P(A)  1
where P(A) = probability of an event A.
3. P(A') = 1 - P(A) where A' is the complement of A.
P(A) + P(A’) = 1
4. The intersection of A and B, written A  B, whose outcomes belong to
both A and B where
5. Events A and B are said to be mutually exclusive if they have no
outcomes in common.
Eg: P(A  B) = 0.
P(A  B) = 0
6. The union of A and B , written as
A  B , event whose outcomes belong to either A or B or both.
P(A  B) = P(A) + P(B) - P(A  B)
If A and B are mutually exclusive, P(A  B) = P(A) + P(B).
7. A and B are independent events if P(A  B) = P(A) P(B)
n(S)
n(A)
P(A) 2. 
S events in items of no.
A event in items of no.

A
n(S)
B) n(A
B) P(A

 
   B A
A B
B

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1.3 Probability Approach
Ways to express the sample space
i. X & Y axis
ii. Tree Diagram
iii. Venn Diagram
iv. Contingency table
v. Own imagination
Examples: