Assignment 1 Subject: Probability & Statistics (mas291)
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Assignment 1 Subject: Probability & Statistics (MAS291) Group: …………………. NOTE: Font: Times new roman, 13. Margins: Top: 2cm, Bottom: 2cm, Left: 3cm, Right: 2cm. Font Math Type: Times new roman, 13. Question 1 (10 marks). If A, B, and C are mutually exclusive events with and determine the following probabilities: (a) (b) (c) (d) (e) . Question 2 (10 marks). The probability that a vehicle entering the Luray Caverns has Canadian license plates is 0.12; the probability that it is a camper is 0.28; and the probability that it is a camper with Canadian license plates is 0.09. What is the probability that (a) a camper entering the Luray Caverns has Canadian license plates? (b) a vehicle with Canadian license plates entering the Luray Caverns is a camper? (c) a vehicle entering the Luray Caverns does not have Canadian plates or is not a camper? Question 3 (10 marks). A batch of 350 samples of rejuvenated mitochondria contains 8 that are mutated (or defective). Two are selected from the batch, at random, without replacement. (a) What is the probability that the second one selected is defective given that the first one was defective? (b) What is the probability that both are defective? (c) What is the probability that both are acceptable? Question 4 (10 marks). A paint-store chain produces and sells latex and semigloss paint. Based on long-range sales, the probability that a customer will purchase latex paint is 0.75. Of those that purchase latex paint, 60% also purchase rollers. But only 30% of semigloss paint buyers purchase rollers. A randomly selected buyer purchases a roller and a can of paint. What is the probability that the paint is latex? Question 5 (10 marks). The thickness of wood paneling (in inches) that a customer orders is a random variable with the following cumulative distribution function: (a) (b) (c) (d) (e) Question 6 (10 marks). In testing a certain kind of truck tire over rugged terrain, it is found that 25% of the trucks fail to complete the test run without a blowout. Of the next 15 trucks tested, find the probability that (a) from 3 to 6 have blowouts; (b) fewer than 4 have blowouts; (c) more than 5 have blowouts. Question 7 (10 marks). Suppose the probability that any given person will believe a tale about the transgressions of a famous actress is 0.8. What is the probability that (a) the sixth person to hear this tale is the fourth one to believe it? (b) the third person to hear this tale is the first one to believe it? Question 8 (10 marks). The probability of a successful optical alignment in the assembly of an optical data storage product is 0.8. Assume that the trials are independent. (a) What is the probability that the first successful alignment requires exactly four trials? (b) What is the probability that the first successful alignment requires at most four trials? (c) What is the probability that the first successful alignment requires at least four trials? Question 9 (10 marks). Suppose that lesions are present at 5 sites among 50 in a patient. A biopsy selects 8 sites randomly (without replacement). (a) What is the probability that lesions are present in at least one selected site? (b) What is the probability that lesions are present in two or more selected sites? (c) Instead of eight sites, what is the minimum number of sites that need to be selected to meet the following objective? The probability that at least one site has lesions present is greater than or equal to 0.9. Question 10 (10 marks). Cabs pass your workplace according to a Poisson process with a mean of five cabs per hour. Suppose that you exit the workplace at 6:00 p.m. Determine the following: (a) Probability that you wait more than 10 minutes for a cab. (b) Probability that you wait fewer than 20 minutes for a cab. (c) Mean number of cabs per hour so that the probability that you wait more than 10 minutes is 0.1. ……………………. End ……………………. Download 59.65 Kb. Share with your friends:
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