1. Statistics for Managers 5th Edition
Chapter 4
Basic Probability 1

2. Chapter Topics Basic probability concepts Conditional probability
Sample spaces and events, simple probability, joint probability
Conditional probability
Statistical independence, marginal probability
Bayes’s Theorem 2

3. Terminology Experiment- Process of Observation
Outcome-Result of an Experiment
Sample Space- All Possible Outcomes of a Given Experiment
Event- A Subset of a Sample Space 3

4. Sample Spaces Collection of all possible outcomes
e.g.: All six faces of a die:
e.g.: All 52 cards in a deck: 4

5. Events Simple event Joint event
Outcome from a sample space with one characteristic
e.g.: A red card from a deck of cards
Joint event
Involves two outcomes simultaneously
e.g.: An ace that is also red from a deck of cards 5

6. Visualizing Events Contingency Tables Tree Diagrams Black 2 24 26
Ace Not Ace Total
Black
Red
Total
Ace
Red
Cards
Not an Ace
Full
Deck
of Cards
Ace
Black
Cards 6
Not an Ace

7.  Special Events Impossible event Complement of event
Null Event
Impossible event
e.g.: Club & diamond on one card draw
Complement of event
For event A, all events not in A
Denoted as A’
e.g.: A: queen of diamonds A’: all cards in a deck that are not queen of diamonds  7

8. Contingency Table A Deck of 52 Cards Red Ace Total Ace Red 2 24 26
Not an
Ace
Total
Ace
Red 2 24 26
Black 2 24 26
Total 4 48 52
Sample Space 8

9. Tree Diagram Event Possibilities Ace Red Cards Not an Ace Full Deck
of Cards
Ace
Black
Cards
Not an Ace 9

10. Probability
Certain
Probability is the numerical measure of the likelihood that an event will occur
Value is between 0 and 1
Sum of the probabilities of all mutually exclusive and collective exhaustive events is 1 1 .5
Impossible 10

11. Types of Probability Classical (a priori) Probability
P (Jack) = 4/52
Empirical (Relative Frequency) Probability
Probability it will rain today = 60%
Subjective Probability
Probability that new product will be successful 11

12. Computing Probabilities
The probability of an event E:
Each of the outcomes in the sample space is equally likely to occur
number of event outcomes
P(E)=
total number of possible outcomes in sample space
n(E)
n(S) =
e.g. P( ) = 2/36
(There are 2 ways to get one 6 and the other 4) 12

13. Probability Rules 1 0 ≤ P(E) ≤ 1
Probability of any event must be between 0 and1
2 P(S) = 1 ; P(Ǿ) = 0
Probability that an event in the sample space will occur is 1; the probability that an event that is not in the sample space will occur is 0
3 P (E) = 1 – P(E)
Probability that event E will not occur is 1 minus the probability that it will occur 13

14. Rules of Addition Special Rule of Addition
P (AuB) = P(A) + P(B) if and only if A and B are mutually exclusive events
General Rule of Addition
P (AuB) = P(A) + P(B) – P(AnB)

15. Rules Of Multiplication
Special Rule of Multiplication
P (AnB) = P(A) x P(B) if and only if A and B are statistically independent events
General Rule of Multiplication
P (AnB) = P(A) x P(B/A) 15

16. Conditional Probability Rule
P(B/A) = P (AnB)/ P(A)
This is a rewrite of the formula for the general rule of multiplication. 16

17. Bayes Theorem
P(B1) = probability that Bill fills prescription = .20
P(B2) = probability that Mary fills prescription = .80
P(A B1) = probability mistake Bill fills prescription = 0.10
P(A B2) = probability mistake Mary fills prescription = 0.01
What is the probability that Bill filled a prescription that contained a mistake? 17

18. Bayes’s Theorem
Adding up the parts of A in all the B’s
Same Event 18

19. Bayes Theorem (cont.) P(B1 A) = (.20) (.10) (.20) (.10) + (.80) (.01)
.02
.028
.71
71% 19

20. Bayes Theorem (cont.) Bill fills prescription Mary fills prescription
(Prior) Bi
.20
. 80
1.00
(Conditional)
.10
.01
A Bi
(Joint)
A  Bi
.020
.008
P(A) =.028
(Posterior)
Bayes
.02/.028=.71
.008/.028=.29
1.00 20

21. Chapter Summary Discussed basic probability concepts
Sample spaces and events, simple probability, and joint probability
Defined conditional probability
Statistical independence, marginal probability
Discussed Bayes’s theorem 21