26and27_AdditionalStudyQuestions - ACC 333 (Farrell)...

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ACC 333 (Farrell) Classes 26 & 27 Fall 2011 Page 1 of 7 Additional Study Questions Probability and Decision Trees 1. Parts Problems A manufacturing firm receives shipments of parts from two different suppliers, Ace Company and Action Company. Currently, 65% of the parts purchased by the company are from Ace, and the remaining are from Action. The quality of the purchased parts varies with the source of supply. Based on historical data, the conditional probabilities of receiving good and bad parts are: Good Parts Bad Parts Ace Company .98 .02 Action Company .95 .05 If a part is found to be bad, what is the probability that it came from Ace? From Action? 2. Prospect Fields in Oil and Gas An oil company’s geological assessment indicates that there’s a 25% chance that a particular prospect field will produce oil. Further, there’s an 80% chance that a particular well will strike oil given that oil is present in the field. Suppose that one well is drilled on the field and it comes up dry. What is the probability that the prospect field will produce oil? 3. Predicting the Weather Suppose that you believe the chance that it will rain is 30%. When you are watching television, the weather person tells you that it’s going to rain tomorrow. Suppose that you know that the weather person is pretty good, and makes mistakes only 10% of the time. In other words, if it’s actually going to rain tomorrow the weather person says it’s going to rain with probability 0.9 and says it’s not going to rain with probability 0.1; if it’s not going to rain tomorrow she says it’s going to rain with probability 0.1 and says it’s not going to rain with probability 0.9. Using Bayes’ Theorem, calculate what the probability of rain tomorrow is after hearing the weather person’s prediction that it will rain. 4. Screening for Disease Suppose there is a screening test for a rare disease, and that one person in 10,000 actually has the disease. The screening test used to show if a person has the disease is quite good --- if a person has the disease the test will come back positive with certainty, and if a person does not have the disease the test will give a negative result 99 times out of 100, but will one time out of 100 (that is, with probability 0.01) give a positive result (a “false positive”). If a randomly selected person is tested and the test result is positive, use Bayes’ Theorem to determine the probability that the person actually has the disease.
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ACC 333 (Farrell) Classes 26 & 27 Fall 2011 Page 2 of 7 5. Rosetta Stone Exploration Co. has obtained information that suggests that an unusual formation of malachite might be found in the Sonora Desert. The deposit will cost $15 million for rights, permits, and development.
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This note was uploaded on 03/19/2012 for the course ACCACC 333 taught by Professor Anne during the Fall '11 term at Miami University.

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26and27_AdditionalStudyQuestions - ACC 333 (Farrell)...

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