1. Chapter 4: Basic Probability
Chapter Goal:
Explain basic probability concepts and definitions
Use contingency tables to view a sample space
Apply common rules of probability
Compute conditional probabilities
Determine whether events are statistically independent

2. Definitions:
Probability – the chance or likelihood that an uncertain (particular) event will occur
Probability is always between 0 and 1, inclusive
There are three approaches to assessing the probability of un uncertain event:
1. a priori classical probability– based of a prior knowledge
2. empirical classical probability– based on observed data
3. subjective probability -- an individual judgment or opinion about the probability of occurrence

3. Basic Concepts: Sample Space – the collection of all possible events
An Event – Each possible type of occurrence or outcome from the sample space
Simple Event – an event that can be described by a single characteristic
Complement of an event A -- All outcomes that are not part of event A
Joint event --Involves events that can be described by two or more characteristics simultaneously

4. Basic Concepts: Continued
Mutually exclusive events: Events that cannot occur together
Collectively exhaustive events
One of the events must occur
The set of events covers the entire sample space
The probability of any event must be between 0 and 1, inclusively. That is: 0 ≤ P(A) ≤ 1 for any event A
The sum of the probabilities of all mutually exclusive and collectively exhaustive events is 1 exhaustive. That is, if A, B, and C are mutually exclusive and collectively exhaustive event, then (the entire sample space)

5. Contingency Tables: A sample space can be presented by a C.T.
It is very useful for the study of empirical probabilities
Example: Let’s say 400 managers were surveyed about booking airline tickets and researching prices of tickets in the internet
Sample Space: Total Number of Managers Surveyed
Booked Airline Ticket in the Internet
Yes, B1
No, B2
Totals
Researched Prices in the Internet
Yes, A1 88
124
212
No, A2 20
168
188
108
292
400

6. Computing Simple (Marginal) Probobilities.
Where B1, B2, …, Bk are k mutually exclusive and collectively exhaustive events
Probability of a joint event, A and B:
How many simple events are in my example?
How many joint events are in my example?

7. Rules of Probability: General Addition Rule
P(A or B) = P(A) + P(B) - P(A and B)
If A and B are mutually exclusive, then
P(A and B) = 0, so the rule can be simplified
P(A or B) = P(A) + P(B)
If A and B are collectively exhaustive, then
P(A or B) = P(A) + P(B)=1

8. A conditional probability is the probability of one event, given that another event has occurred:
The conditional probability of A given that B has occurred
The conditional probability of B given that A has occurred
Where P(A and B) = joint probability of A and B
P(A) = marginal probability of A
P(B) = marginal probability of B

9. Multiplication Rule– for two events A and B
Two events A and B are statistically independent if the probability of one event is unchanged by the knowledge that other even occurred. That is:
Then the multiplication rule for two statistically independent events is:

10. Let look at problem 4.26, page 148