1. Chapter 5 A Survey of Basic Statistics Probability Concepts
for Business and Economics
Fifth Edition
Chapter 5
A Survey of
Probability Concepts
Douglas William Samuel
Irwin/McGraw-Hill 1 1 1 2 1 1

2. Topics Covered Probability definition Experiment, outcome, and event
Approaches to Assigning Probabilities;
- Classical Probability
- Subjective Probability
- Empirical
Some rules for computing probabilities 2 2 2 2 3 2

3. Probability What is Probability ?
We often use this term in our daily lives. Like there is 50% chance of raining, or there is 70% chance of increasing stock prices…
Probability; Is a value between zero to one, describing the relative possibility an event will occur. 2 2 2 2 3 2

4. Subjective Probability
Estimating the chance of getting A in this course
Estimating the probability GE will lose its number one ranking of selling cars to Ford Motors. 2 2 2 2 3 2

5. Experiment: A fair die is cast.
example
Experiment: A fair die is cast.
Possible outcomes: The numbers 1, 2, 3, 4, 5, 6
One possible event: The occurrence of an even number. That is, we collect the outcomes 2, 4, and 6. 2 2 2 3 2 2

6. Subjective probability is based on whatever information is available.
There are three definitions of probability: classical, empirical, and subjective.
The Classical definition applies when there are n equally likely outcomes.
The Empirical definition applies when the number of times the event happens is divided by the number of observations.
“based on the past”
Subjective probability is based on whatever information is available.
“when no past experience” 2 2 2 3 2 2

7. Classical Probability
Consider an experiment rolling of a die. What is the probability of the event ”an even number of spots face up” ???
The possible outcome;
Probability of even number = = 50% 6
Possible of even numbers face up 2 2 2 2 3 2

8. Empirical Probability
Throughout her teaching career Professor Jones has awarded 186 A’s out of 1,200 students. What is the probability that a student in her section this semester will receive an A? 2 2 2 2 3 2

9. Some rules for Computing Probability
Computing the probability of two or more events by applying rules of :
1- Rules of addition
2- Rules of multiplication 2 2 2 2 3 2

10. Some rules for Computing Probability
1- Special Rules of addition; states that the Probability of A or B occurring equals the sum of their respective probabilities.
Example; in the die-tossing experiment is the events of ;
A “ an number 4 or larger”
B “ an number of 2 or smaller”
Then applying Rules of addition formula;
P(A or B) = P (A) + P (B) 2 2 2 2 3 2

11. Some rules for Computing Probability
Example;
Weight Event # of packages Probability of
occurrence
Underweight A %
Satisfactory B , %
Overweight C % %
What is the probability that a particular package will be either underweight or overweight . Applying special rule of addition?
P(A or c) = P (A) + P (c)
= 2.5% + 7.5% = 10%
100
4000 2 2 2 2 3 2

12. Some rules for Computing Probability
1- Rules of addition
A special case where there is joint probability.
Joint probability; two or more event happen concurrently or at the same time which is not mutually exclusive.
Example; Suppose that Florida Tourist commission selected a sample of 200 tourists who visits USA. The survey revealed that 120 tourists went to Disney world (A), and 100 went to Busch Gardens (B). So 120/200 = 60% and 100/200 = 50% with 110%. To explain the situation that some visitors visit both locations, in this case we have to determine the joint probabilities, suppose it = 30% then the formula:
P( A or B) = P(A) + P(B) – P( Both A & B)
= 60% + 50% - 30% = 80% 2 2 2 2 3 2

13. Some rules for Computing Probability
2- Rules of multiplication
When two events happening at the same time and they have no affect on each others, they are independent.
Example; Tossing two coins , the outcomes of the first one is not affected by the other.
Formula;
P(A) and (P) = P(A)P(B) 2 2 2 2 3 2

14. Contingency tables
Back in chapter 4, we point out a relationship between two variables.
Example; a sample of executives was surveyed about their loyalty to the company.
One of the questions was “ if you were given an offer by another company equal to or slightly better than your present position, would you remain with the company or take the other position?”
The responses of the 200 executives in the survey were classified with their length of service. 2 2 2 2 3 2

15. Contingency tables Length of service less than 1-5 6-10 More than
1 year years years years Loyalty B B B B Total
Would remain, A
Would not remain,A
What is the probability of randomly selecting an executive who is loyal to the company (would remain) and who has more than 10 years of service? 2 2 2 2 3 2

16. Tree Diagrams
Is a graph that is helpful in organizing calculations that involve several stages. Each segment in the tree is one stage of the problem. 2 2 2 2 3 2

17. Tree Diagrams . Less than 1 year 10/200 = 5% 1-5 years 30/200 = 15%
Would
remain
120/200
6-10 years 5/ = 2.5%
Over 10 years75/ = 37.5%
Less than 1 year 25/200 = 12.5%
80/200
1-5 years 15/ = 7.5%
Would
not
remain
6-10 years 10/ = 5%
Over 10 years 30/ = 15%
100% 2 2 2 2 3 2

18. The Multiplication Formula
When there is m ways of doing one thing and n ways of doing another thing, mXn ways of doing both. Example;
Dr. Delong has 10 shirts and 8 ties. How many shirt and tie outfits does he have?
(10)(8) = 80 2 2 2 2 3 2

19. The Permutation Formula
Is applied to find the possible number of arrangements when there is only one group.
Example; A machine operator must make four safety checks before starting his machine. It does not matter in which order the check are made. In how many different ways can the operator make the checks ?
Formula:
n is the total number of objects
r is the number of objects selected
n! is n factorial 2 2 2 2 3 2

20. The Permutation Formula
Example; compute the following
6! 3! 4!
= (3.2.1) = 180
Example; there are three electronic parts to be assembled , so n=3. all of the three to be inserted in plug-in unit, r=3. 2 2 2 2 3 2