Section 6 2 2 Probability Models AP Statistics

Section 6. 2. 2 Probability Models AP Statistics November 25, 2009 Berkley High School todd 1@toddfadoir. com AP Statistics, Section 6. 2, Part 2

Notation AP Statistics, Section 6. 2, Part 2 2

Probability Rules: Rule 1 AP Statistics, Section 6. 2, Part 2 3

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

Probability Rules: Rule 3 AP Statistics, Section 6. 2, Part 2 5

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

Probability Rules: Rule 4 (Different Notation) AP Statistics, Section 6. 2, Part 2 7

Example Marital status: Never married Married Widowed Divorced Probability: . 298 . 622 . 005 . 075 n What is P(Married)? ¨ P(Married)=. 622 AP Statistics, Section 6. 2, Part 2 8

Example Marital status: Never married Married Widowed Divorced Probability: . 298 . 622 . 005 . 075 n What is P(not Married)? ¨ P(not Married)= 1 -. 622=. 378 (Complement Rule) AP Statistics, Section 6. 2, Part 2 9

Example Marital status: Never married Married Widowed Divorced Probability: . 298 . 622 . 005 . 075 n 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 10

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. n The probabilities of any event is the sum of the probabilities of the outcomes making up the event. n AP Statistics, Section 6. 2, Part 2 11

Benford’s Law is the distribution of first digits in tax records, payment records, invoices, etc. n This distribution is handy in spotting illegitimate records. n AP Statistics, Section 6. 2, Part 2 12

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

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

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

Equally Likely Outcomes AP Statistics, Section 6. 2, Part 2 16

Assignment n Exercises: 6. 19 -6. 23 AP Statistics, Section 6. 2, Part 2 17