1.Review Ch 14 2.Ch 14 Partner Quiz 3.Notes on Ch 15 part 1 We will review conditional probability, then we will learn how to test for independence, and calculate probabilities for events that draw without replacement. AgendaObjective CH 15 CONDITIONAL PROBABILITY AND INDEPENDENCE PART 1

The probability that one event happens or that another event happens. Apply the General Addition Rule P(A U B) = P(A) + P(B) - P(A∩B) CONDITIONAL PROBABILITY

Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% a blood test, and 22% both tests. What is the probability that a randomly selected DWI suspect is given… A test? A blood test or a breath test, but not both? Neither test? EXAMPLE

The probability that one event happens given that another event is already known. Apply the General Multiplication Rule P(A∩B) = P(A) ∙ P(B│A) … Without replacement. CONDITIONAL PROBABILITY

Scenario 1: Your favorite flavor is pink, what is the probability the you draw a pink? Scenario 2: Two people get to draw before you, one draws an orange the other draws a pink. What are your chances now of drawing a pink? EXAMPLE.. MRS. KENNEDY HAS A BAG OF STARBURSTS. THERE ARE 10 RED, 12 ORANGE, 8 YELLOW, AND 6 PINK.

Scenario 1: What is the probability of drawing three face cards in a row, with replacement? Scenario 2: What is the probability of drawing three face cards in a row, WITHOUT replacement? EXAMPLE: STANDARD DECK OF CARDS

Provide the statistics to calculate simple and conditional probabilities. CONTINGENCY TABLES Pierced Ears? YesNoTotal Male Female84488 Total

CONTINGENCY TABLES Pierced Ears? YesNoTotal Male Female84488 Total What is the probability that a student picked at random is male? 2.What is the probability that a student picked at random is pierced? 3.What is the probability that a student picked at random is a pierced male? 4.What is the probability that a student picked at random is pierced or male?

CONTINGENCY TABLES Pierced Ears? YesNoTotal Male Female84488 Total What is the probability that a student is male given the student is pierced? 2.What is the probability that a student picked at random is pierced given he is male? 3.What is the probability that a student picked at random is a pierced given the student is female? 4.What is the probability that a student picked at random is female given she is pierced?

CONDITIONAL PROBABILITY

What is the probability that a student is male given he is pierced? What is the probability that a student is pierced given the student is female? CONTINGENCY TABLES Pierced Ears? YesNoTotal Male Female84488 Total

CONTINGENCY TABLES Grade Level SchoolABBelow B Liberal Arts Engineering Health What is the probability that a student received below a B? 2.What is the probability that a student is in engineering given he has below a B? 3.What is the probability that a student picked at random has lower than a B, given he is in engineering? 4.Which of these conditional probabilities tells you whether this college’s Engineering students tend to earn low grades than liberal arts or Health?

IF P(A∩B) = P(A) X P(B) when independent and ….. P(A∩B) = P(B) X P(B│A) as a general rule. By substitution…. P(B│A) = P(B) confirms independence. INDEPENDENCE??

Is piercing independent of gender? CONTINGENCY TABLES Pierced Ears? YesNoTotal Male Female84488 Total

P(A U B) = P(A) + P(B) – P(A ∩ B) GENERAL ADDITION RULE

Example: Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% a blood test, and 22% both tests. What is the probability that a randomly selected DWI suspect is given…. a)A test? b)A blood test or a breath test, but not both? c)Neither test? GENERAL ADDITION RULE

Example: Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is What’s the probability that an American chosen at random has…. a)Traveled to Canada but not Mexico? b)Traveled to either Canada or Mexico? c)Not traveled to either country? GENERAL ADDITION RULE

Disjoint events do not share any occurrences, therefore there is no intersection of events. Use Addition Rule OR P(A U B) P(A) + P(B) Independent events are events in which the occurrence of one event does not affect the other. Use Multiplication Rule AND P(A ∩ B) P(A) X P(B) INDEPENDENT VS. DISJOINT

What is the probability a card drawn is an ace or red? DISJOINT OR INDEPENDENT ?

Two cards are drawn without replacement. What is the probability they are both aces? DISJOINT OR INDEPENDENT ?

Are a “red card” and “spade independent or mutually exclusive? DISJOINT OR INDEPENDENT ?

Are “red card” and “ace” independent? Mutually exclusive? DISJOINT OR INDEPENDENT ?

Are “face card” and “king” independent? Mutually exclusive? DISJOINT OR INDEPENDENT ?

JeansOtherTotal Male12517 Female81119 Total INDEPENDENCE?? What is the probability that a male wears jeans?

JeansOtherTotal Male12517 Female81119 Total INDEPENDENCE?? What is the probability that someone wearing jeans is a male?

JeansOtherTotal Male12517 Female81119 Total INDEPENDENCE?? Are being male and wearing jeans disjoint? Are sex and attire independent?