1. Mr. Reider AP Stat November 18, 2010
Sections 6.1 and 6.2
Mr. Reider
AP Stat
November 18, 2010

2. Drill
What is probability? What does it mean to be random?

3. Section 6.1
Randomness

4. Definitions
We call a phenomenon random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions.
The probability of any outcome of a random phenomenon is the proportion of time the outcome would occur in a very long series of repetitions.

5. Probability Model A probability model consist of two parts:
A sample space
A way of assigning probabilities to events

6. Section 6.2
Probability Models

7. Sample Space
The Sample Space (denoted S) of a random phenomenon is the set of all possible outcomes.

8. What is the Sample Space of…
Flipping a coin?
Rolling a die?
Drawing a card from a standard deck?

9. Multiplication Principle
If you can do one task in a number of ways and a second task in b number of ways, then both tasks can be done in a ∙ b number of ways.
What if we are doing three tasks? Four tasks?
Tree diagrams

10. Example
Flipping a coin and rolling a die

11. Simple Set Theory Intersection: Denoted Read “A and B” Union: Denoted
Read “A or B”

12. Events An event is an outcome, or set of outcomes, of a sample space.
An event, E, is a subset S. What does it mean to be a subset?

13. Events
The complement of any event is that A does not occur. It is denoted AC.

14. Events
Two events are considered disjoint if they have no common outcomes.
Note: “disjoint” and “mutually exclusive” are synonymous

15. Notation

16. Probability Rules Let A and B be events
Addition Rule: If A and B are disjoint, then

17. Probability in a Finite Sample Space
If there are a finite set of outcomes in S, we can assign a probability to each individual outcome.
What conditions do we need to meet with these probabilities?

18. Example What is P(Married)? Marital status: Never married Married
Widowed
Divorced
Probability:
.298
.622
.005
.075
What is P(Married)?
P(Married)
=.622

19. Example What is P(not Married)? Marital status: Never married Married
Widowed
Divorced
Probability:
.298
.622
.005
.075
What is P(not Married)?
P(not Married) =
=.378 (Complement Rule)

20. Example What is P(Never married or Divorced)? Marital status:
Widowed
Divorced
Probability:
.298
.622
.005
.075
What is P(Never married or Divorced)?
Since “Never married and Divorced are disjoint, P(Never married or Divorced) =
=.373 (Addition Rule for disjoint events)

21. Equally Likely Outcomes
If a random phenomenon has k possible out comes, all of them equally likely, then each individual outcome has a probability of The probability of any event A is

22. Independent Events
Two events are considered independent if knowing that one event occurs does not change the probability of the other occurs.
What do you think are some examples of independent events?
Rolling a number cube twice, flipping a coin twice, drawing two cards with replacement, winning a contest.

23. Multiplication Rule
If A and B are independent events, then

24. Probability Rules Let A and B be events
Addition Rule: If A and B are disjoint, then
Multiplication Rule: If A and B are mutually exclusive, then

25. Examples A = {rolling a 2 or 5 on a die.}
B = {Drawing a face card from a standard deck of playing cards}
C= {Rolling a 3 or 4 and drawing an ace}

26. Example