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

2. Events
Simple 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

3. 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
Not an Ace

4. Simple and Joint Events
The Event of a Triangle
The event of a triangle AND blue in color
There are 5 triangles in this collection of 18 objects
Two triangles that are blue

5.  Special Events 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 

6. Special Events Mutually exclusive events
Two events cannot occur together
e.g. -- A: queen of diamonds; B: queen of clubs
Events A and B are mutually exclusive
Collectively exhaustive events
One of the events must occur
The set of events covers the whole sample space
e.g. -- A: all the aces; B: all the black cards; C: all the diamonds; D: all the hearts
Events A, B, C and D are collectively exhaustive
Events B, C and D are also collectively exhaustive

7. Probability
Sample of 1,000 households in terms of purchase behaviour for big-screen TV sets.

8. Decision Tree

9. Sample of 300 households whether the TV set purchased was an HDTV and whether they also purchased a DVD player.
Draw the decision tree for purchased a DVD player and an HDTV.

10. Joint Probability Using Contingency Table
Event
Event B1 B2
Total A1
P(A1 and B1)
P(A1 and B2)
P(A1) A2
P(A2 and B1)
P(A2 and B2)
P(A2)
Total
P(B1)
P(B2) 1
Marginal (Simple) Probability
Joint Probability

11. Computing Compound Probability
Probability of a compound event, A or B:

12. Compound Probability (Addition Rule)
P(A1 or B1 ) = P(A1) + P(B1) - P(A1 and B1)
Event
Event B1 B2
Total A1
P(A1 and B1)
P(A1 and B2)
P(A1) A2
P(A2 and B1)
P(A2 and B2)
P(A2)
Total
P(B1)
P(B2) 1
For Mutually Exclusive Events: P(A or B) = P(A) + P(B)

13. Computing Conditional Probability
The probability of event A given that event B has occurred:

14. Conditional Probability and Statistical Independence
Multiplication rule:

15. Conditional Probability and Statistical Independence
Events A and B are independent if
Events A and B are independent when the probability of one event, A, is not affected by another event, B

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

17. Bayes’s Theorem Using Contingency Table
Fifty percent of borrowers repaid their loans. Out of those who repaid, 40% had a college degree. Ten percent of those who defaulted had a college degree. What is the probability that a randomly selected borrower who has a college degree will repay the loan?

18. Bayes’s Theorem Using Contingency Table
Repay
Repay
Total
College .2
.05
.25 .3
.45
.75
College
Total .5 .5
1.0