ECON114 APPLICATIONS FOR PROBABILITY
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ECON114
APPLICATIONS FOR PROBABILITY
1. Equal numbers ofmotor vehicles turn north and turn south from the entrance ramps of a major highway. Draw a tree diagram which shows, for the next three motor vehicles approaching the highway, how many could turn north, and how many could turn south. In how many cases could
there be
a. exactly two vehicles that turn north
b. exactly one vehicle that turns north
c. exactly three vehicles that turn south
d. exactly three vehicles that turn north
2. An examination consists of 10 multiple-choice questions, each with 4 choices (1 of which is correct and 3 incorrect).
Which kind of counting method should be used?
a. In how many ways can a student mark the answers to these questions if 1 choice is made for each of the 10 questions?
How many choices for each question?
b. How many ways can the student get a perfect score (all correct) on this examination?
How many choices for “correct” in each question?
c. How many ways can the student mark the answers to these questions, marking all 10 questions incorrectly?
How many choices for “in correct” in each
question?
3. A manager can evaluate a subordinate as outstanding, excellent, average, below average, or poor.
Which kind of counting method should be used?
a. In how many ways can a manager evaluate four subordinates as either excellent or outstanding (not using any other evaluation categories)?
How many evaluation categories for each
subordinate?
b. In how many ways can the manager evaluate four subordinates, using all five evaluation categories?
How many evaluation categories for each
subordinate?
4. Among six men and four women accountants employed by an accounting firm, two will be offered promotions to positions as partners. In how many ways can the partnerships be offered to
Which kind of counting method should be used?
a. any two of the accountants and hence, write conclusion
b. two of the male accountants and hence, write conclusion
c. one male accountant and one female accountant, and hence, write conclusion
d. zero male accountants, and hence, write conclusion
The same expression as zero male accountants and
two female accountants
5. The Institutional Investor ranks the top 10 institutions according to assets under management - the institution's own as well as those of their clients. In order of size these are Prudential Insurance Co., American Express Co., Metropolitan Life, Bankers Trust Co., Equitable Investment Corp., J.P. Morgan & Co., Citicorp, Wells Fargo & Co., Aetna Life Insurance Co., and Mellon Bank Corp.
Which kind of counting method should be used?
a. How many permutations are there of 3 ofthese 10 institutions? State your conclusion.
b. How many permutations are there of2 ofthe 3 largest institutions? State your conclusion.
6. In a plan to balance its budget, C stands for the event that the city will cut expenditures, and R is the event that the city will raise revenues. State in words what probabilities are expressed by
a. P(C') b. P(R') c. P(C R)
d. P(C R) e. P(C' R) f. P(C' R)
7. If F and S are the events that a magazine publisher will launch a new fashion magazine or a new sports magazine, and P(F) = 0.35 and P(S) = 0.25, find the probability that the publisher
Rules of probability
a. will not launch the fashion magazine
b. will launch the fashion magazine or the sports magazine
c. will launch neither the fashion magazine nor the sports magazine
8. A self-employed mason knows from experience that 45 percent of his contracts for brickwork are for common (American) bond, 35 percent for English bond, and 20 percent for Flemish bond. Bonding provides various patterns, which arrange the bricks to lap over each other in order to stagger the vertical joints. Also, 60 percent ofthe mason's contracts for common bond are for residential construction, 35 percent ofthe contracts for English bond are for residential construction, and
40 percent ofthe contracts for Flemish bond are for residential construction. Ifthe mason signs a contract to provide brickwork for a residence, what are the revised probabilities that the job is not for common bond?
Which method should be used to calculate the
conditional probability?
2022-03-19