WARM - UP After an extensive review of weather related accidents an insurance company concluded the following results: An accident has a 70% chance of occurring during a Rain storm; a 85% chance of occurring during a Snow storm; a 58% of occurring during Fog; 6% during a Windy day, and a 0.3% chance of occurring during a Clear day. It is estimated that it rains 9% of the time, snows 0.1% of the time, fog 22% of the time, just wind 32% of the time, and the remaining being clear days. (a) Draw a TREE diagram of the event. (b) Does it appear that Accidents and Weather Conditions are Independent? JUSTIFY! (c) What is the probability that an accident will occur? (d) If an accident has occurred, what is the probability that it was raining that day?  

A=0.70 (a) Draw a TREE diagram of the event. (b) Does it appear that Accidents and Weather Conditions are Independent? JUSTIFY! (c) What is the probability that an accident will occur? (d) If an accident has occurred, what is the probability that it was raining that day? R=0.09 A=0.85 S=0.001 A=0.58 F=0.22 A=0.06 W=0.32 A=0.003 C=0.369

Joint probability: P(A∩B) = P(A)∙P(B) If two events, A and B, are INDEPENDENT, then the following are true: Joint probability: P(A∩B) = P(A)∙P(B) Conditional prob.: P(A|B) = P(A|C) = P(A)

Quiz Review Define P-Value Five multiple choice questions, each with four possible answers, appear on an exam. What is the probability that if you just guess, you a. ) get at least one of the questions wrong? b.) get all of the questions correct? A store reports that 5 out of 15 shirts are mediums. What is the probability that at least 1 medium shirt will be sold from the next 4 customers. You roll a fair die six times. What is the probability that you roll at least one 5? What is the probability of rolling a 5 six times in a row. You toss a coin 3 times and note the number of times a tail is obtained. List the sample Space for # of tails you could obtain out of 3 tosses AND comment on if all outcomes are equally likely. 7. There is a 12% chance that you will get into college A and a 30% chance of getting into college “B”. Getting accepted at both college happens 3.6% of the time. Given that you get into College A there is a 30% chance you get into College B. Is acceptance into these colleges Mutually Exclusive (disjoint) events , Independent events or Neither? Explain using a mathematical explanation. 8. In a business class, 20% of the students have never taken a statistics class, 42% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that both of the first two groupmates you meet have studied at least one semester of statistics?

Quiz Review P-Value: Five multiple choice questions, each with four possible answers, appear on an exam. What is the probability that if you just guess, you a. ) get at least one of the questions wrong? b.) get all of the questions correct? A store reports that 5 out of 15 shirts are mediums. What is the probability that at least 1 medium shirt will be sold from the next 4 customers. You roll a fair die six times. What is the probability that you roll at least one 5? What is the probability of rolling a 5 six times in a row. 6. You toss a coin 3 times and note the number of times a tail is obtained. List the sample Space for # of tails you could obtain out of 3 tosses AND comment on if all outcomes are equally likely. The probability of obtain extreme results (Ha), given Ho is True. =.999023 =.000977 =.8462 =.6651 =0.00002143 {0, 1, 2, 3} 1 2 HHH HHT HTH HTT 1 2 3 THH THT TTH TTT NOT equally likely,

Quiz Review There is a 12% chance that you will get into college A and a 30% chance of getting into college “B”. Getting accepted at both college happens 3.6% of the time. Given that you get into College A there is a 30% chance you get into College B. Is acceptance into these colleges Mutually Exclusive (disjoint) events , Independent events or Neither? Explain using a mathematical explanation. 8. In a business class, 20% of the students have never taken a statistics class, 42% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that both of the first two groupmates you meet have studied at least one semester of statistics? P(A∩B) = ?? = 0 P(A∩B) = ?? = P(A)∙P(B) P(B|A) = ?? = P(B) P(No Stats) = 0.20 P(At least one Stat) = 1 - None P(1 Stat) = 0.42 P(2+ Stats) = 0.38

Page 364: #23, 24, 40, 44, 46

Page 364: #23, 24, 40, 44, 46

P(Luggage)=P(On time ∩ Luggage)+P(Not on time ∩ Luggage) PAGE 366 #35 a) The probability that the luggage makes the connection is dependent on whether or not the flight is on time. The probability is 0.95 if the flight is on time, and only 0.65 if it is not on time. b) P(Luggage)=P(On time ∩ Luggage)+P(Not on time ∩ Luggage) =(0.15)(0.95)+(0.85)(0.65) =0.695

0.467 PAGE 366 #46 P(Supplier A | Defective) = P(Defective) (0.7)(0.01) . (0.7)(0.01)+(0.2)(0.02)+(0.1)(0.04) 0.467