1. Chapters 14/15 AP Statistics Mrs. Wolfe
PROBABILITY RULES
Chapters 14/15
AP Statistics
Mrs. Wolfe

2. What is probability? Probability is the long run relative frequency
of some occurrence
Probability of event A = P(A)
P(A)= number of successful outcomes
number of total outcomes

3. Example 1:
Imagine that a bowl contains the following Marbles: 4 green, 2 blue, 3 white, 1 red. P(Green) = ? P(Red or blue)= ? P(not white) = ? P (green and blue)= ?

4. Important words in Probability
OR—means to add
also means the UNION(U) of sets A and B
P(A U B) = P(A) + P(B)- P(A∩ B)

5. AND--means to multiply
2nd Important Word
AND--means to multiply
also means the INTERSECTION (∩)
of sets A and B
P(A ∩ B) = P(A) ∙ P(B)
assumes A and B are INDEPENDENT

6. NOT—means to subtract from 1 or from 100%
3rd Important Word
NOT—means to subtract from 1 or from 100%
A c or Ā or A’=the complement of A
P(Ac) = 1 – P(A)

7. KEY VOCABULARY
Trial—a single attempt of a random occurrence Outcome—the value measured or observed for an individual trial Event—a collection of outcomes-designated with capital letters A, B, C, etc. Sample Space—collection of all outcomes possible

8. TYPES OF PROBABILITY Theoretical—mathematical computation
involved to determine what should happen
Empirical—experiment performed to count
chance of event happening
Subjective—educated guess –no real
probability theory used

9. LAW OF LARGE NUMBERS
In the long run, empirical probability will settle down toward the theoretical probability. Does not mean that the “Law of Averages” will be true…just because a coin hasn’t been heads in 5 tries, it still has a 50% chance of being heads on the next try!

10. PROPERTIES OF PROBABILITY
Probability of all outcomes must sum to 1.
2. 0 < P(x) < 1

11. EXAMPLE USING VENN DIAGRAMS
Police reports that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% a blood test and 22% are given both tests. What is the probability of a. a test? b. a blood test or a breath test, but not both? c. neither test?

12. Important Event Concepts
Disjoint Events—also called mutually exclusive means that A and B share no common outcomes Independent Events—how one event occurs does not affect the probability of the second event

13. Independent? Mutually exclusive?
Given P(A) = 0.6 and P(B) = 0.3. P (A U B) = Are A and B mutually exclusive? P(A ∩ B) = Are A and B independent?

14. Blood type problem
45% type O, 40% type A, 11% type B, 4% type AB What is the probability of a person being Type A and Type O? What is the probability of two persons in a row being Type A?

15. Car Problem Review
Suppose 40% of cars in your area are manufactured in the US, 30% in Japan, 10% in Germany and 20% in other countries. If a car is selected at random, find a. P(car not US made) b. P(car from Japan or Germany) c. P(two cars in a row from Japan) d. P(at least one of three cars is US made)

16. CONDITIONAL PROBABILITY-CHART
Public Private Total Male Female Totals