Prob_MasterExercises

# Prob_MasterExercises - Hit escape to return to the lecture...

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Unformatted text preview: Hit escape to return to the lecture slides Axioms of Probability • After an exam, a doctor decides that a patient has either plague, leprosy, or SARS. She decides that the probability is 0.7 that the patient has plague, 0.2 that the patient has leprosy, and 0.1 that the patient has SARS. What is the probability that the patient has either plague or leprosy? (Assume that it’s not possible to have multiple illnesses at once) P0001 Solution Hit escape to return to the lecture slides • Prove that: P A ∪ B ( 29 = P A ( 29 + P B ( 29- P A ∩ B ( 29 Axioms of Probability P0002 Solution Hit escape to return to the lecture slides • Are these valid probabilities? Why or why not? – A: -0.53 – B: 0.42 – C: 1.03 Axioms of Probability P0003 Solution Hit escape to return to the lecture slides • Suppose that a test for cancer is 99% sensitive and 85% specific and that the prevalence of cancer in the test population is 3%. What is the positive predictive value of the test, P(D| +)? – A: 85% – B: 75% – C: 17% – D: Don’t know Bayes P0004 Solution Hit escape to return to the lecture slides • Suppose that a test for cancer is 99% sensitive and 85% specific and that the prevalence of cancer in the test population is 3%. What is the negative predictive value of the test, P(D c | -)? – A: 75% – B: 99% – C: 3% – D: Don’t know Bayes P0005 Solution Hit escape to return to the lecture slides • A face recognition system has been developed to detect intruders. A prototype system has been installed outdoors at a biowarfare research facility. Based on a series of controlled tests, the following information is available: Given that the intruder was detected by the system, the weather was clear 75% of the time, cloudy 20% of the time, and raining 5% of the time. When the system failed to detect the intruder, 60% of the days were clear, 30% cloudy, and 10% rainy. If overall there is a 90% chance detecting an intruder, what is the probability that the system will detect her given rainy weather conditions? – A: 82% – B: 95% – C: 5% – D: Don’t know Bayes P0006 Solution Hit escape to return to the lecture slides Bernoulli • List as many examples as you can of Bernoulli random variables. P0007 Solution Hit escape to return to the lecture slides Binomial • In your research on chronic bronchitis you notice that children develop chronic bronchitis in the first year of life in 3 out of 20 households where they live with a parent who has chronic bronchitis. By comparison, the national incidence is 5%. How likely are infants in at least three out of 20 households to develop chronic bronchitis if the probability for any one household is 5%? – A: 0.0596 – B: 0.0754 – C: 0.1500 – D: Don’t Know P0008 Solution Hit escape to return to the lecture slides Binomial • If 20% of the nanoparticles produced by a new technique are defective, what is the probability that of 4 chosen at random that exactly 1 will be defective?...
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## This note was uploaded on 02/01/2011 for the course BME 335 taught by Professor Dunn during the Spring '10 term at University of Texas.

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Prob_MasterExercises - Hit escape to return to the lecture...

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