1. recall
• Probability
• Mutually Exclusive Events
• Independent Events
• Collectively Exhaustive Events
• Three Approaches to Probability
• Classical
• Empirical
• Subjective

2. Seatwork discussion
PERSON 1 PERSON 2
YES YES
YES NO
NO YES
NO NO

3. Seatwork discussion
PART 1 PART 2
ACCEPTABLE ACCEPTABLE
REPAIRABLE
SCRAPPED
REPAIRABLE ACCEPTABLE
REPAIRABLE
SCRAPPED
SCRAPPED ACCEPTABLE
REPAIRABLE
SCRAPPED

4. Seatwork discussion
a) 6/34 = 3/17
b) Empirical

5. Seatwork discussion
a) 2/5 or 0.4
b) Empirical

6. Seatwork discussion
a) Empirical
b) Classical
c) Classical
d) Empirical

7. Seatwork discussion
a) Since gender equity is being considered, the company cannot promote two
people of the same gender. Since there are 6 men and 3 women, the
outcomes are as follows:
Woman 1 Woman 1 Woman 1
Man 1 Woman 2 Man 3 Woman 2 Man 5 Woman 2
Woman 3 Woman 3 Woman 3
Woman 1 Woman 1 Woman 1
Man 2 Woman 2 Man 4 Woman 2 Man 6 Woman 2
Woman 3 Woman 3 Woman 3
b) Classical

8. Seatwork discussion

9. A Survey of Probability
Concepts
Lesson 4.2
Taken from: http://highered.mcgraw-
hill.com/sites/0073401781/student_view0/

10. Joint Probability – Venn
Diagram
JOINT PROBABILITY A probability that measures the
likelihood two or more events will happen
concurrently.
10

11. Rules for Computing
Probabilities
Rules of Addition
• Special Rule of Addition - If two events A
and B are mutually exclusive, the
probability of one or the other event’s
occurring equals the sum of their
probabilities.
P(A or B) = P(A) + P(B)
• The General Rule of Addition - If A and B
are two events that are not mutually
exclusive, then P(A or B) is given by the
following formula:
P(A or B) = P(A) + P(B) - P(A and B)
11

12. Addition Rule - Example
What is the probability that a card chosen at random from a
standard deck of cards will be either a king or a heart?
P(A or B) = P(A) + P(B) - P(A and B)
= 4/52 + 13/52 - 1/52
= 16/52, or .3077
12

13. Try this:
A B
18 7 25
If there are 60 scores in all,
1. Find P(A), P(B), P(A and B).
2. What is P(A or B)?

14. The Complement Rule
The complement rule is used to
determine the probability of an
event occurring by subtracting
the probability of the event not
occurring from 1.
P(A) + P(~A) = 1
or P(A) = 1 - P(~A).
14

15. Example:
1. The events A and B are mutually exclusive.
Suppose P(A) = 0.30 and P(B) = 0.20.
• What is the probability of either A or B occurring?
• What is the probability that neither A nor B will
happen?
2. A study of 200 advertising firms revealed their
income after taxes:Taxes
Income after Number of Firms
Under $1 million 102
$1-20 million 61
$20 million or more 37
• What is the probability an advertising firm selected at

16. Seatwork:
1. The chairman of the board says, ―There is a 50%
chance this company will earn a profit, a 30%
chance it will break even and a 20% chance it will
lose money next quarter. Find P(not lose money
next quarter) and P(break even or lose money).
2. If the probability that you get a grade of A in
Statistics is 0.25 and the probability you get a B is
0.50, find a) P(not getting an A), b) P(getting an A
or B) and c) P(getting lower than a B)
3. Find the probability that a card drawn from a
standard deck is a heart or face card (K, Q, J)?

17. Special Rule of
Multiplication
• The special rule of multiplication requires that
two events A and B are independent.
• Two events A and B are independent if the
occurrence of one has no effect on the
probability of the occurrence of the other.
• This rule is written: P(A and B) = P(A)P(B)
17

18. Multiplication Rule-
Example
A survey by the American Automobile association (AAA) revealed 60
percent of its members made airline reservations last year. Two
members are selected at random. What is the probability both made
airline reservations last year?
Solution:
The probability the first member made an airline reservation last year is
.60, written as P(R1) = .60
The probability that the second member selected made a reservation is
also .60, so P(R2) = .60.
Since the number of AAA members is very large, you may assume that
R1 and R2 are independent.
P(R1 and R2) = P(R1)P(R2) = (.60)(.60) = .36
18

19. Conditional Probability
A conditional probability is the
probability of a particular event
occurring, given that another event
has occurred.
The probability of the event A given
that the event B has occurred is
written P(A|B).
19

20. General Multiplication Rule
The general rule of multiplication is used to find the joint
probability that two events will occur.
Use the general rule of multiplication to find the joint
probability of two events when the events are not
independent.
It states that for two events, A and B, the joint probability that
both events will happen is found by multiplying the
probability that event A will happen by the conditional
probability of event B occurring given that A has occurred.
20

21. General Multiplication Rule - Example
A golfer has 12 golf shirts in his closet. Suppose 9 of these shirts are white and
the others blue. He gets dressed in the dark, so he just grabs a shirt and
puts it on. He plays golf two days in a row and does not do laundry.
What is the likelihood both shirts selected are white?
21

22. General Multiplication Rule - Example
• The event that the first shirt selected is white is W1. The
probability is P(W1) = 9/12
• The event that the second shirt selected is also white is
identified as W2. The conditional probability that the
second shirt selected is white, given that the first shirt
selected is also white, is P(W2 | W1) = 8/11.
• To determine the probability of 2 white shirts being
selected we use formula: P(AB) = P(A) P(B|A)
• P(W1 and W2) = P(W1)P(W2 |W1) = (9/12)(8/11) = 0.55
22

23. exercise:
• The board of directors of Company A consists of 8
men and 4 women. A four-member search
committee is to be chosen at random to conduct a
nationwide search for a new company president.
• What is the probability that all four members of the
search committee will be women?
• What is the probability that all four members will be
men?

24. Contingency Tables
A CONTINGENCY TABLE is a table used to classify sample
observations according to two or more identifiable
characteristics
E.g. A survey of 150 adults classified each as to gender and the
number of movies attended last month. Each respondent is
classified according to two criteria—the number of movies
attended and gender.
24

25. Contingency Tables -
Example
A sample of executives were surveyed about their loyalty to their
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 cross-classified with their length of service with the
company.
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? 25

26. Contingency Tables -
Example
Event A1 happens if a randomly selected executive will remain with
the company despite an equal or slightly better offer from
another company. Since there are 120 executives out of the 200
in the survey who would remain with the company
P(A1) = 120/200, or .60.
Event B4 happens if a randomly selected executive has more than
10 years of service with the company. Thus, P(B4| A1) is the
conditional probability that an executive with more than 10 years
of service would remain with the company. 75 of the 120
executives who would remain have more than 10 years of
service, so P(B4| A1) = 75/120.
26

27. Try this
• What is the probability of selecting an executive with
more than 6-10 years of service?
• What is the probability of selecting an executive who
would not remain with the company given that he has 6
to 10 years of service? Who is loyal or less than 1 year
service?
• What is the probability of selecting an executive who has
6 to 10 years of service and who would not remain with
the company?

28. QUIZ
Open Notes
10 minutes to review

29. Answer the following on a piece of paper.
1. The market research department at a company plans to survey teenagers about
a newly developed soft drink. Each will be asked to compare it with his/ her
favorite drink.
a. What is the experiment?
b. What is one possible outcome?
c. What is a possible event?
2. There are 90 students who will graduate from Treston High School. Fifty of them
are planning to go to college. Two students are to be picked at random to carry
the flag at graduation.
a. What is the probability that both students are planning to go to college?
b. What is the probability that only one plans to go to college? (hint: Find
P(student1 goes to college OR student1 does not go to college))
3. In a management trainee program, 80% of the participants are female. Ninety
percent of the females attended college and 78% of the males attended college.
a. What is the probability of randomly picking a female who has not attended
college when choosing at random?
b. Are gender and college attendance independent? Explain.
c. If there were 1000 participants in all, construct a contingency table showing
both variables.