# Q9 - Solutions to Practice Problems for Part II 1 A fund...

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Solutions to Practice Problems for Part II 1. A fund manager is considering investment in the stock of a health care provider. The manager's assessment of probabilities for rates of return on this stock over the next year are summarized in the accompanying table. Let A be the event "Rate of return will be more than 10%" and B the event "Rate of return will be negative." RATE OF RETURN Less than - 10% - 10% to 0% 0% to 10% 10% to 20% More than 20% PROBABILITY .04 .14 .28 .33 .21 a. Find the probability of event A . A P 20% than More 20% o t 10% P 21 0 33 0 . . 54 0 . b. Find the probability of event B . B P 0% to 10% - 10% than Less P 14 0 04 0 . . 18 0 . c. Describe the event that is the complement of A . A is the event in which "Rate of return will be no more than 10%". d. Find the probability of the complement of A . A P A P 1 54 0 1 . 46 0 . e. Describe the event that is the intersection of A and B . B A is the event in which the rate of return is both more than 10% and less than zero.

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Managerial Statistics 730 Prof. Juran f. Find the probability of the intersection of A and B . It is impossible for the rate of return both to be more than 10% and less than zero, so: 0 B A P g. Describe the event that is the union of A and B . B A is the event in which the rate of return is either more than 10% or less than zero. h. Find the probability of the union of A and B . B A P 0% to 10% - 10% - than less 20% than more 20% to 10% P 14 0 04 0 21 0 33 0 . . . . 72 0 . i. Are A and B mutually exclusive? Yes; they can't both occur at the same time. j. Are A and B collectively exhaustive? No. If, for example, the rate of return is 5%, then neither A nor B has occurred. 2. A manager has available a pool of eight employees who could be assigned to a project-monitoring task. Four of the employees are women and four are men. Two of the men are brothers. The manager is to make the assignment at random, so that each of the eight employees is equally likely to be chosen. Let A be the event "chosen employee is a man" and B the event "chosen employee is one of the brothers." a. Find the probability of A . A P employees men n n 8 4 5 0 .
Managerial Statistics 731 Prof. Juran b. Find the probability of B . B P employees brothers n n 8 2 25 0 . c. Find the probability of the intersection of A and B . B A P employees men and brothers n n 8 2 25 0 . d. Find the probability of the union of A and B . B A P employees brothers or men n n 8 4 5 0 . 3. A department store manager has monitored the numbers of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the table. Let A be the event "There will be at least one complaint in a week," and B the event "There will be less than 10 complaints in a week." NUMBER OF COMPLAINTS 0 1-3 4-6 7-9 10-12 More than 12 PROBABILITY .14 .39 .23 .15 .06 .03 a.

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• Spring '15
• Michael Parzen
• Probability, Probability theory, probability density function, Prof. Juran

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