1. Statistics and Quantitative Analysis U4320
Segment 3: Probability
Prof. Sharyn O’Halloran

2. Review Descriptive Statistics

4. Statistics

5. Example: Employment

6. How raw data maps into a frequency table

8. Probability Theory Simple Probability Property: As N gets large
The relative frequency with which events occur when repeated many times.
 Property: As N gets large

9. Example: Toss a coin 3 times
Outcome Space
Simple probability- The frequency of A divided by the total number of outcomes.

10. Compound Events
A and B
Example: What is the probability of exactly two heads AND having the first toss be heads?
Definition: The relative frequency of the events that meet both criteria

11. A or B
 Example: What is the probability of getting either exactly 2 heads or no heads at all?
  Definition: The probability of A or B is the relative frequency of the events that meet either criteria.

12. Conditional Probability (A given B)
Example: What is the probability that the first toss is a head given that there are exactly two heads?
 Denote: P(1st H/2H)
 Definition:

13. Probability Tables

14. Independence
Definition: The occurrence of one event does not affect the probability of the other.
P(A|B) = P(A)
Example:
20% of the students play football, 50% play basketball, and 15% play both. How can we put this into a table?

15. What's the probability that a student selected at random will:
a) Play neither sport?
b) Play football or basketball?
c) Are playing basketball and football independent?