1. Chapter 15 Probability Rules!
General Addition Rule
Conditional Probability

2. Recall… for any Random phenomenon each trial generates an outcome
An event is a set of outcomes
The collection of all possible outcomes is called the SAMPLE SPACE (S)

3. Sample Space
List the sample space and tell whether you think they are equally as likely
Toss 2 coins; record the order of heads and tails
A family has 3 children; record the number of boys
Flip a coin until you get a head or 3 consecutive tails
Roll two dice; record the larger number

4. Drawing Venn Diagrams
Real Estate ads suggest that 64% of homes for sale have garages, 21% have swimming pools, and 17% have both features. What is the probability that a home for sale has
a pool or a garage?
neither a pool nor a garage?
a pool but no garage?

5. General Addition Rule
Does NOT require disjoint events

6. Conditional Probabilities
A Gallup survey of June 2004 asked 1005 U.S. adults who they think better fits their idea of what a first lady should be, Laura Bush or Hillary Clinton.
What is the probability that the person thought Laura Bush best fits their first lady ideals?
What is the probability that the person is younger than 50?
What is the probability that the person is younger than 50 and thinks Clinton is a better fit?
What is the probability that the person is younger than 50 or thinks Clinton is a better fit?
18-29
30-49
50-64
over 65
total
Clinton
135
158 79 65
437
Bush 77
237
112 92
518
Neither 5 21 14 10 50
Total
217
416
205
167
1005

7. Conditional Probability
“The probability of B given A”

8. Conditional Probabilities
You draw a card at random from a standard deck of 52 cards. Find the following conditional probabilities.
the card is a heart, given that it is red.
the card is red, given that it is a heart
the card is an ace, given that it is red
the card is a queen given that it is a face card

9. Chapter 15 Probability Rules!
*General Multiplication Rule
*Testing for Disjoint/Independence
*Probability Tables
*Tree Diagrams

10. General Multiplication Rule
** when A and B are INDEPENDENT, then **
When A and B are NOT independent, then
Which event you define as A or B does not matter

11. How do we know if two event are INDEPENDENT??
If P(B|A) = P(B), then A and B are independent Example: Is good grades as a goal independent of gender??
Goals
Gender
Grades
Popular
Sports
Total
Boy
117 50 60
227
Girl
130 91 30
251
247
141 90
478

12. Events can NOT be disjoint AND independent Consider
Event A = {making the team}
Event B = {not making the team}

13. Probability Tables
Construct a probability table with the given information. Suppose 78% of DUI suspects are given a breath test, 36% a blood test, and 22% of DUI suspects receive both tests.

14. Are giving a DUI suspect a blood test and a breath test mutually exclusive (disjoint)?
Are giving the 2 tests independent?

15. Drawing without Replacing
Suppose you are drawing cards from a standard deck.
What is the probability you will draw 3 spades in a row??

16. Data on College Binge Drinking
37% drink moderately
19% abstain completely
Of those who binge drink: 17% car accidents
Of those who drink moderately: 9% car accidents
FIND: P(college student who binge drinks and has been involved in a car accident)

17. Tree Diagram shows sequence of events make when using GMR
covers all possible outcomes
probabilities should add up to 1

18. Reversing the Conditions
What is the probability the student is a binge drinking given they were in an accident.
Tree Diagram given P(accident|binge drinker)
Use the tree to find P(binge|accident)