This document summarizes key concepts from Chapter 4 of Allan G. Bluman's textbook "Elementary Statistics: A Step-by Step Approach" including: - Defining probability experiments, outcomes, events, and sample spaces - Calculating classical and empirical probabilities - Using addition and multiplication rules to find probabilities of compound events - Defining and calculating conditional probability - Using fundamental counting rules and permutations/combinations to calculate number of possible outcomes The document provides examples for each concept to illustrate their application.

1. Chapter 4 Probability & Counting Rules Reference: Allan G. Bluman (2004) Elementary Statistics: A Step-by Step Approach . New York : McGraw Hill

4. Tree Diagram for Tossing Two Coins First Toss H T H T H T Second Toss

5. Sample Spaces - Examples

7. Formula for Classical Probability

11. Complement of an Event E

14. Rule for Complementary Event P E P E or P E P E or P E P E ( ) ( )   1 1 1 ( ) =  ( ) ( ) + ( ) = .

16. Formula for Empirical Probability

18. Empirical Probability - Example Type Frequency A B AB O 22 5 2 21 50 = n

21. The Addition Rules for Probability A B A and B are mutually exclusive

22. Addition Rule 1 When two events A and B are mutually exclusive, the probability that A or B will occur is P A or B P A P B ( ) ( ) ( )  

25. Addition Rule 2 When two events A and B are not mutually exclusive, the probability y that A or B will occur is P A or B P A P B P A and B ( ) ( ) ( ) ( )   

26. Addition Rule 2 A B A and B (common portion)

28. Addition Rule 2 - Example

33. Multiplication Rule 1

39. Multiplication Rule 2

45. Tree Diagram for Example P ( B 1 ) 1/2 Red Red Blue Blue Box 1 P ( B 2 ) 1/2 Box 2 P ( R | B 1 ) 2/3 P ( B | B 1 ) 1/3 P ( R | B 2 ) 1/4 P ( B | B 2 ) 3/4 (1/2)(2/3) (1/2)(1/3) (1/2)(1/4) (1/2)(3/4)

47. Conditional Probability - Formula

51. Conditional Probability - Example

56. Tree Diagrams - Example Cincinnati Bus New York Pittsburgh Plane Train Bus Boat Auto Bus Boat Boat Bus Auto Auto Plane, Bus Plane, boat Plane, auto Train, bus Train, boat Train, auto Bus, bus Bus, boat Bus, auto