1. Section 6.2.2 Probability Models
AP Statistics
November 25, 2009
Berkley High School

2. AP Statistics, Section 6.2, Part 2
Notation
AP Statistics, Section 6.2, Part 2

3. Probability Rules: Rule 1
AP Statistics, Section 6.2, Part 2

4. Probability Rules: Rule 2
AP Statistics, Section 6.2, Part 2

5. Probability Rules: Rule 3
AP Statistics, Section 6.2, Part 2

6. Probability Rules: Rule 4
AP Statistics, Section 6.2, Part 2

7. Probability Rules: Rule 4 (Different Notation)
AP Statistics, Section 6.2, Part 2

8. AP Statistics, Section 6.2, Part 2
Example
Marital status:
Never married
Married
Widowed
Divorced
Probability:
.298
.622
.005
.075
What is P(Married)?
P(Married)=.622
AP Statistics, Section 6.2, Part 2

9. AP Statistics, Section 6.2, Part 2
Example
Marital status:
Never married
Married
Widowed
Divorced
Probability:
.298
.622
.005
.075
What is P(not Married)?
P(not Married)= =.378 (Complement Rule)
AP Statistics, Section 6.2, Part 2

10. AP Statistics, Section 6.2, Part 2
Example
Marital status:
Never married
Married
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)
AP Statistics, Section 6.2, Part 2

11. Probabilities in a finite space
Assign a probability to each individual outcome. These probabilities must be numbers between 0 and 1 and must have sum of 1.
The probabilities of any event is the sum of the probabilities of the outcomes making up the event.
AP Statistics, Section 6.2, Part 2

12. AP Statistics, Section 6.2, Part 2
Benford’s Law
Benford’s Law is the distribution of first digits in tax records, payment records, invoices, etc.
This distribution is handy in spotting illegitimate records.
AP Statistics, Section 6.2, Part 2

13. AP Statistics, Section 6.2, Part 2
Example
First Digit 1 2 3 4 5 6 7 8 9
Probability:
.301
.176
.125
.097
.079
.067
.058
.051
.046
AP Statistics, Section 6.2, Part 2

14. AP Statistics, Section 6.2, Part 2
Example
First Digit 1 2 3 4 5 6 7 8 9
Probability:
.301
.176
.125
.097
.079
.067
.058
.051
.046
AP Statistics, Section 6.2, Part 2

15. AP Statistics, Section 6.2, Part 2
Example
First Digit 1 2 3 4 5 6 7 8 9
Probability:
.301
.176
.125
.097
.079
.067
.058
.051
.046
AP Statistics, Section 6.2, Part 2

16. Equally Likely Outcomes
AP Statistics, Section 6.2, Part 2

17. AP Statistics, Section 6.2, Part 2
Assignment
Exercises:
AP Statistics, Section 6.2, Part 2