1. The Practice of Statistics, Fourth Edition.
Probability Rules!!!
Section 5.2
Reference Text:
The Practice of Statistics, Fourth Edition.
Starnes, Yates, Moore
Lesson 6.1.1

2. Objectives Probability Models Basic Probability Rules Addition Rule
Sample Space -Probability Model Event
Basic Probability Rules
Compliment “not A” -Mutually exclusive (disjoint)
Addition Rule
P(A or B) =P(A) + P(B)
Two way tables
Venn Diagrams
Intersections and Unions.

3. Probability Models Some lingo to get down
Toss a coin. What are the possible outcomes?
A: Heads or tails! This is what's know as our sample space
Roll a regular 6-sided die. What are the possible outcomes?
____ ____ _____ _____ ____ ____
Probability model: some chance process that consists of two parts: Sample space S, and probability for each one…. Lets look at rolling two 6-sided die! What are the outcomes?

5. Events
With the two dice rolled, we could find any collection of outcomes and their probabilities.
This is what’s known as an Event- any collection of outcomes from some chance process. Events are assigned capital letters such as A,B,C
P(A) where A= sum of 5.

6. Compliment

7. Lets try some more! A = sum of 5 B = sum is not 5 C = sum is 6
Find the probability of the following:
P(A)= P(B)=
P(C)= P(A or C)=
- Notice how P(A) +P(B) = 1

8. Basic Rules of Probability

9. Mutually Exclusive (disjoint)
Two events are mutually exclusive if they have no outcomes in common and so can never occur together.
Example: if one event occurs in 40% of all trials, and a different event occurs in 25% of the trials, and the two can never occur together, then one or the other occurs on 65% of the trials.
40% + 25% = 65%

10. Check for Understanding
Chose an American adult at Random. Define two events:
A = the person has a cholesterol level of 240 milligrams per deciliter of blood (mg/dl) or above. (High cholesterol)
B= The person has a cholesterol level of 200 to 239 (borderline high cholesterol)
According to the American Heart Association:
P(A) = 0.16 and P(B) = 0.29
Explain why events A and B are mutually exclusive.
Say in plain language what the event “A or B” is. What is P(A or B)?
If C is the event that a person chosen has normal cholesterol (below 200 mg/dl) what's P(C)

11. Two way Tables
Students in college stats class wanted to find out how common it is for young adults to have their ears pierced. They recorded data on two variables- gender and whether the student had a pierced ear – for all 178 people in class. The two way table below displays the data.
Pierced ears?
Gender
Yes No
Total
Male 19 71 90
Female 84 4 88
103 75
178

12. A= male B= pierced ears
Suppose we chose a student from the class at random. Find the probability that the student
(a) has pierced ears
(b) is a male with pierced ears
(c) is male or has pierced ears

13. Venn Diagrams Event A P(A) = 90/178 Event B P(B) = 103/178
P(A and B) = 19/178

14. Venn Diagram General Addition Rule
The Venn Diagram suggests to fix this “double counting”
P(A or B) = P(A) + P(B) – P(A and B)
= 90/ /178 – 19/178
= 174/178

15. Intersection and Unions
If we are talking about “A and B” then we can also call this the intersection of A and B. The corresponding notation is A П B
If we are talking about “A or B” then we can also call this the Union of A and B. The corresponding notation is A U B

16. Venn Diagram: Intersection and Unions

17. Objectives Probability Models Basic Probability Rules Addition Rule
Sample Space -Probability Model Event
Basic Probability Rules
Compliment “not A” -Mutually exclusive (disjoint)
Addition Rule
P(A or B) =P(A) + P(B)
Two way tables
Venn Diagrams
Intersections and Unions.

18. Test Results! Grade: Amount: Marginal % ……A......……....1.……….5%
…….B…………...9……...47% 68% Passed
…….C…………..3..……...16%
…….D…………..5.……...26%
…….F… ………..5% 31% Failed
Mean: 79% Max: 92% Min: 58% No Outliers

19. Tracking AP Stats 2014-2015 (WHS)
Ch. 1 Test Ch. 2 Test Ch. 3 Test Ch. 4 Test
A 5 A 5 A3 A1
B5 B 6 B5 B9
C6 C 4 C6 C3
D2 D 1 D2 D5
F1 F 2 F2 F1

20. Homework
Worksheet