Problem Set 2

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California Polytechnic State University, San Luis Obispo *

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Economics

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Feb 20, 2024

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1.) P(j) 0.4 P(d) 0.25 P(jnd) 0.15 Find or P(j)+P(d)-P(jnd)= 0.5 2.) A.) P(A)= 0.45 P(B)= 0.35 Yes, they are mutually exclusive. 0.8 B.) 1 P(B)= 0.65 3.) A study of 100 students who had been awarded university scholarships showed that 40 had part-time jobs, 25 had made the dean’s list the previous semester, and 15 had both a part time job and made the dean’s list. What was the probability that a student had a part-time job or was on the dean’s list? Let A be an event that a person’s primary method of transportation to and from work is an automobile and B be an event that a person's primary method od transportation to and from work in a bus. Suppose that in a large city P(A)=0.45 and P(B)=0.35 Are events A and B mutually exclusive? What is the probability that a person's uses an automobile or a bus in going to and from work? Find the probability that a person's primary method of transortation is some means other than a bus. P(B c )= According to Census Bureau deaths in the United States occur at a rate of 2,425,000 per year. The National Center for Health Statistics reported that the three leading causes of death during 1997 were heart disease (725,790), cancer (537,390), and stroke (159,877). Let H, C, and S represent the events that a person dies of heart disease, cancer, and stroke respectivley.

A.) Estimate P(H), P(C), and P(S). P(H)= 0.299295 P(C)= 0.221604 P(S)= 0.065929 B.) P(HnC)=P(H)*P(C) P(HnC) 0.066325 C.) P(HuC)=P(H)+P(C)-P(HnC) P(HUC)= 0.454574 D.) P(O)= 0.413172 4.) A.) Develop a joint probability table using these data. Other Total 1929 Full Time 0.218248 0.203733 0.039399 0.461379 Part time 0.207361 0.307413 0.023847 0.538621 Total 0.425609 0.511146 0.063245 1 B.) of heart disease, cancer, and stroke respectivley. Are events H and C mutually exclusive (assume independece)? Find P(HnC). What is the probability that a person dies from heart disease or cancer? What is the probability that a person dies from a cause other than one of these three causes? In a survey of MBA students, the following data obtained on "Students" first reason for application to the school in which they were matriculated. School Quality School Cost/Conv enience Use the marginal probabilities of school quality, school cost or convenience, and other to comment on the most important reason for choosing a school.

P(CC)= 0.511146 The biggest likelyhood for choosing a school seems to be Cost/Conveinence C.) P(F/SQ)= 0.473034 D.) P(P/SQ)= 0.384986 E.) P(B)= 0.425609 P(B/A)= 0.922472 P(B)=/P(B/A) they are dependent; P(B)=/P(B/A) 5.) A.) P(AnB)=P(A)*P(B) -> Independent P(AnB)=P(A)*P(B) -> 0.1925 B.) P(AuB)=P(A)+P(B)-P(AnB) P(AuB)=P(A)+P(B)-P(AnB) 0.71 C.) reason for choosing a school. If a student goes full time, what is the probability that school quality will be the first reason for choosing a school? If a student goes part time, what is the probability that school quality will be the first reason for choosing a school? Let A be the event that a student is full time and B the event that the student lists school quality as the first reason for applying. Are events A and B independent? Justify your answer. A purchasing agent has placed a rush order for a particular raw material with two different suppliers, A and B. If neither order arrives in 4 days the production process must be shutdown until at least one of the orders arrives. The probability that supplier A can deliever the material in 4 days is 0.55. The probability that supplier B can deliever the material in 4 days is 0.35. What is the probability that both suppliers deliever the material in 4 days? Because two separate suppliers are involved, assume independece? What is the probability that at least one supplier delievers the material in 4 days?

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1-P(AuB)= 0.29 6.) What is the probability the production process is shut down in 4 days because of a shortage in raw materials? 6. A consulting firm has submitted a bid for a large research project. The firm’s management initially felt there was a 50-50 chance of getting the bid. However, the agency to which the bid was submitted has subsequently requested additional information on the bid. Experience indicates that on 75% of the successful bids and 40% of the unsuccessful bids, agency requested additional information. a) What is the prior probability the bid will be successful (i.e., prior to receiving the request for additional information)? b) What is the conditional probability of a request for additional information, given that the bid will ultimately be successful? c) Compute a posterior probability that the bid will be successful given that a request for additional information has been received? (It is very useful to build the probability tree that leads you to the application of the Bayes Theorem). 4

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