RGRRR RGRRRG GRRRRR WARM - UP The Die has Four Green and Two Red sides Which of the following has the highest probability of occurring? RGRRR RGRRRG GRRRRR

48 Determine the NUMBER of outcomes in the following Sample Space 1. Spin the spinner once, flip a single coin, and toss a die. 48 {RH1, RH2, RH3, RH4, RH5, RH6, RT1, RT2, RT3, RT4, RT5, RT6, GH1, GH2, GH3, GH4, GH5, GH6, GT1, GT2, GT3, GT4, GT5, GT6, YH1, YH2, YH3, YH4, YH5, YH6, YT1, YT2, YT3, YT4, YT5, YT6, BH1, BH2, BH3, BH4, BH5, BH6, BT1, BT2, BT3, BT4, BT5, BT6} 2. What is the Probability of getting a Blue or Green, Tail, AND a Prime Number?

Formal Probability - Notation P(A or B) = P(A  B) “add”  = Union P(A and B) = P(A  B) “mult.”  = Intersection A = {1, 2, 3, 4, 5, 6, 7, 8} B = {3, 6, 9, 12} C = {15, 18} 1. (A  B) = 2. (A  B) = 3. (A  C) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 12} {3, 6} Ǿ =Empty Set or { }

6. P(At least One) = 1 – P(None). EXAMPLE: A 6 question multiple choice test has four answer choices for each question. If you are completely unprepared, what is the probability that you will get at least ONE question correct?

What is the Probability of Getting a 5? Discrete Probability: Finite Number of Outcomes. Outcomes and their respective Probabilities are known and listable. EXAMPLE: AP Scores: 1 2 3 4 5 Probability: .14 .24 .31 .21 ? 0.10 What is the Probability of Getting a 5? 2. What is the Probability of Passing (3, 4, 5)? 3. What is the Probability of Not getting Yale Credit (<5)? 0.62 0.90

What is the Probability that BOTH students got 5’s? EXAMPLE: AP Scores: 1 2 3 4 5 Probability: .14 .24 .31 .21 0.10 Lets say you encounter TWO students who just got the AP Statistics Exam results… What is the Probability that BOTH students got 5’s? 2. What is the Probability that at least one of them got a 3? (.1) x (.1) = 0.01 1 – (None get a “3”) 1 – (.69)(.69) = 0.5239

A B C D VENN DIAGRAM 55 – 12 = 43 125 – 12 = 113 = 12 1600 – (113+12+43) = D A = 125 students in Calculus. B = 55 students in Statistics C = 12 students in Calc. and Stats. There are 1600 students at the school. Are Events A and B disjoint? How many Students represents (A and B) = ? How many Students represents Ac = ? How many Students represents D = ? NO! 12 1475 1432

Are mutually exclusive events Independent or Dependent? Independent Events: Two events in which the occurrence of one event has NO EFFECT on the other. P(A ∩ B) = P(A)·P(B) Mutually Exclusive Events are disjoint events. Two events can NEVER occur at the same time. This means that: P(A ∩ B) = 0 Are mutually exclusive events Independent or Dependent?

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