Econ2300 assignment: Ch4 Quiz 1. Each month a brokerage house studies various companies and rates each company’s stock as being either “low risk” or “moderate to high risk.” In a recent report, the brokerage house summarized its findings about 26 aerospace companies and 81 food retailers in the following table: Company Type Low Risk Moderate to High Risk Aerospace company 9 17 Food retailer 57 24 ________________________________________ If we randomly select one of the total of 107 companies, find (a) The probability that the company’s stock is moderate to high risk given that the firm is an aerospace company. (Round your answer to 2 decimal places.) P(high|aero) (b) The probability that the company’s stock is moderate to high risk given that the firm is a food retailer.(Round your answer to 2 decimal places.) P(high|food) (c) Determine if the company type is independent of the level of risk of the firm’s stock. (Round your answers to 2 decimal places.) Dependent. For two events to be independent, P(Aero | Low) = P(Aero). P(Aero | Low) = but the P(Aero) = . They are not equal. 2. 29 percent of the employees in a company have managerial positions, and 39 percent of the employees in the company have MBA degrees. Also, 74 percent of the managers have MBA degrees. Using the probability formulas, find the proportion of employees who either have MBAs or are managers. (Round your answer to 2 decimal places.) P(MBA Manager) 3. 10.00 points An investor holds two stocks, each of which can rise (R), remain unchanged (U), or decline (D) on any particular day. Assume that for the first stock (on a particular day) P(R) = .70 , P(U) = .15 , P(D ) = .15 and that for the second stock (on a particular day) P(R) = .65 , P(U) = .20 , P(D ) = .15 Assuming that these stocks move independently, find the probability that both stocks decline; the probability that exactly one stock rises; the probability that exactly one stock is unchanged; the probability that both stocks rise. Both decline Exactly one rises Exactly one unchanged Both rise ________________________________________ 5. 3 out of 3.00 points If two events are independent, we can _____ their probabilities to determine the intersection probability. Multiply Divide Subtract Add 14. 3.00 points Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card? 0.115 0.462 ? 0.231 0.500 0.308 17. 3.00 points A batch of 50 parts contains 6 defects. If two parts are drawn randomly one at a time without replacement, what is the probability that both parts are defective? 0.014 ? 0.012 0.222 0.102 0.120 (6/50) (5/49) = .012 19. 3 out of 3.00 points An advertising campaign is being developed to promote a new bookstore opening in the newest mall development. To develop an appropriate mailing list it has been decided to purchase lists of credit card holders from MasterCard and American Express. Combining the lists they find the following: 40% of the people on the list have only a MasterCard and 10% have only an American Express card. Another 20% hold both MasterCard and American Express. Finally, 30% of those on the list have neither card. Suppose a person on the list is known to have a MasterCard. What is the probability that person also has an American Express Card? .70 .90 .18 .33 .20 We know that P(M n not A)=0.4, P(A n not M)=0.1, P(M n A)=0.2, P(not A n not M)=0.3. And we are looking for P(A|M)=P(A n M)/P(M) P(M)=P(M n not A)+ P(M n A)=0.4+0.2=0.6 P(A|M)=0.2/0.6=1/3=0.33 20. 3 out of 3.00 points What is the probability of rolling a seven with a pair of fair dice? 7/36 1/36 8/36 6/36 3/36 22. 3 out of 3.00 points What is the probability that an even number appears on the toss of a die? 1.00 0.33 0.67 0.25 0.5 23. 3 out of 3.00 points What is the probability of at least one tail in the toss of three fair coins? 7/8 6/8 5/8 1/8 4/8 25. 3.00 points A person has dealt 5 cards from a deck of 52 cards without replacement. What is the probability they are all clubs? 0.0010 0.0769 0.2500 0.0962 ? 0.0005 26. 3 out of 3.00 points A group has 12 men and 4 women. If 3 people are selected at random from the group without replacement, what is the probability that they are all men? 0.0045 0.4219 0.5143 0.3929 0.0156 27. 3 out of 3.00 points Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container: What is the probability that both items are not defective? 0.3750 0.6154 0.3846 0.1500 0.2000 28. 3 out of 3.00 points Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container: What is the probability that one of the items is defective? 0.1500 0.2250 0.0250 0.3000 0.4750 (3/8)*(3/5)+(5/8)*(2/5)=19/40=0.475 30. 3.00 points A pair of dice is thrown. What is the probability that one of the faces is a 3, given that the sum of the two faces is 9? 1/6 1/3 1/36 ? 1/2 1/4 31. 3.00 points Two percent (2%) of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer buys beer. 0.01 0.50 0.005 0.25 ? 0.04 P(C)=0.02, P(B|C)=0.5, P(C|B)=0.25, P(B n C)=P(B|C)*P(C)=0.01 36. 3 out of 3.00 points Employees of a local university have been classified according to gender and job type. If an employee is selected at random what is the probability that the employee is male and salaried staff? .15 .50 .38 .85 .10 38. 3 out of 3.00 points Employees of a local university have been classified according to gender and job type. If an employee is selected at random what is the probability that the employee is female or works as a member of the faculty? 0.73 0.08 0.70 0.33 0.05 42. 3.00 points A survey is made in a neighborhood of 80 voters. 65 were Democrats and 15 were Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability: A male Republican .333 .188 .500 ? .125 .667 (10/80) = .125 44. 3 out of 3.00 points At a certain university, 30% of the students major in zoology. Of the students majoring in zoology, 60% are males. Of all the students at the university, 70% are males. What percentage of the students are males majoring in zoology? 18% 60% 42% 70% 12% P(Z)=0.3, P(M|Z)=0.6 P(M n Z)=P(M|Z)*P(Z)=0.6*0.3=0.18 46. 3.00 points At a certain university, 30% of the students major in zoology. Of the students majoring in zoology, 60% are males. Of all the students at the university, 70% are males. What proportions of the males are majoring in zoology? ? .26 .86 .18 .21 .60 P(Z|M) = .18/.70 = .257 47. 3 out of 3.00 points At a college, 70 percent of the students are women and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. What is the probability that a student is female and a C student? .45 .50 .70 .25 .05 49. 3.00 points At a college, 70 percent of the students are women and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. If the student is male, what is the probability he is a C student? 0.50 0.10 0.05 0.30 ? 0.17

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