Section 6.2.2 Probability Models AP Statistics November 25, 2009 Berkley High School todd1@toddfadoir.com

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

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

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

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

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

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

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

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)= 1-.622=.378 (Complement Rule) AP Statistics, Section 6.2, Part 2

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)= .298+.075=.373 (Addition Rule for disjoint events) AP Statistics, Section 6.2, Part 2

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

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

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

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

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

Equally Likely Outcomes AP Statistics, Section 6.2, Part 2

AP Statistics, Section 6.2, Part 2 Assignment Exercises: 6.19-6.23 AP Statistics, Section 6.2, Part 2