Chapter 12 – Probability and Statistics

1. Chapter 12 – Probability and Statistics 12.1 – The Counting Principle

2. 12.1 – The Counting Principle • Today we will learn how to: • Solve problems involving independent and dependent events • Solve problems involving dependent events

3. 12.1 – The Counting Principle • Outcome – the result of a single trial • Flipping a coin – 2 outcomes – heads or tails • Sample space – set of all possible outcomes • Event – one or more outcomes of a trial • Independent events – events that do not affect one another

4. 12.1 – The Counting Principle • Example 1 • A sandwich menu offers customers a choice of white, wheat, or rye bread with one spread chosen from butter, mustard, or mayonnaise. How many different combinations of bread and spread are possible?

5. 12.1 – The Counting Principle • Notice that in Example 1, there are 3 ways to choose the bread, 3 ways to choose the spread, and 3 · 3 or 9 ways to choose a combination of the two. • This illustrated the Fundamental Counting Principle

6. 12.1 – The Counting Principle • Fundamental Counting Principle • If event M can occur in m ways and is followed by event N that can occur in n ways, then event M followed by event N can occur in m · n ways • If event M can occur in 2 ways and event N can occur in 3 ways, then M followed by N can occur in 2 · 3 or 6 ways • This rule can be extended to any number of events

7. 12.1 – The Counting Principle • Example 2 • The Murray family is choosing from a trip to the beach or a trip to the mountains. The family can select transportation from a car, train, or plane. How many different ways can the family select a destination followed by a means of transportation? • 2 • 5 • 6 • 9

8. 12.1 – The Counting Principle • Example 3 • How many iPhone numeric password codes are possible?

9. 12.1 – The Counting Principle • Dependent Events – the outcome of one event does affect the outcome of another event • The Fundamental Counting Principle applies to dependent events as well

10. 12.1 – The Counting Principle • Example 4 • How many different schedules could a student who is planning to take only four different classes have?

11. 12.1 – The Counting Principle • Factorial – if n is a positive integer, then • n! = n(n – 1)(n – 2)…2 · 1 • ! – symbol for factorial • 5! = 5 · 4 · 3 · 2 · 1

12. 12.1 – The Counting Principle • Independent Events – If the outcome of an event does not affect the outcome of another event, the two events are independent • Tossing a coin and rolling a die are independent events • Dependent Events – If the outcome of an event does affect the outcome of another event, the two events are dependent • Taking a piece of candy from a jar and then taking a second piece without replacing the first are dependent events

13. 12.1 – The Counting Principle HOMEWORK Page 687 #2 – 28