1. Probability Models
Section 6.2

2. Sample Space S
The set of all possible outcomes

3. Event Any outcome or set of outcomes of a random phenomenon
A subset of the sample space

4. Probability Model
A mathematical description of a random phenomenon consisting of two parts
Sample space S
2. A way of assigning probabilities to events

5. 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 ab number of ways

6. Types of Sampling
With replacement
Without replacement

7. Probability Rules
The probability P(A) of any event A is between 0 and 1 inclusive
2. If S is the sample space in a probability model, then P(S) = 1

8. The complement of any event A is the event that A does not occur, written Ac. The complement rule states that
P(Ac) = 1 – P(A).

9. 4. Two events A and B are disjoint (mutually exclusive) if they have no outcomes in common and so can never occur simultaneously. If A and B are disjoint,
P(A or B) = P(A) + P(B).
This is the addition rule for disjoint events.

10. Venn Diagram
Shows the sample space S as a rectangular area and events as areas within S

11. Probabilities in a Finite Sample Space
Assign a probability to each individual outcome, probabilities must be between 0 and 1
Probability of any event is the sum of the probabilities of the outcomes making up the event

12. Equally Likely Outcomes
If a random phenomenon has k possible outcomes, all equally likely, then each individual outcome has probability 1/k

13. Rule 5 Multiplication Rule for Independent Events
Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs
P(A and B) = P(A)P(B)

14. NOTE:
Disjoint events are not independent.

15. Practice Problems
pg. 356 #