Chapter 15 Probability Rules! General Addition Rule Conditional Probability

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)

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

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?

General Addition Rule Does NOT require disjoint events

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

Conditional Probability “The probability of B given A”

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

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

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

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

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

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.

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

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

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)

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

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)