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Conditional probability worksheet2

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This document presents seven probability problems involving conditional probability and Bayes' theorem. The problems cover topics like the probability of an event given another event, the probability of drawing balls of different colors from an urn, and using Bayes' theorem to calculate the probability someone has a disease based on a test result and prior probability information. Solving several of the problems requires using the law of total probability and Bayes' theorem.

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Worksheet: Probability Theory by Fachrur Rozi, M.Si CONDITIONAL PROBABILITY AND BAYES THEOREM 1. At Kennedy Middle School,the probability that a student takes Technology and Spanish is 0.087. The probability that a student takes Technology is 0.68. What is the probability that a student takes Spanish given that the student is taking Technology? 2. At a middle school,18% of all students play footballand basketball and 32% of all students play football.What is the probability that a student plays basketball given that the student plays football? 3. In Indonesia, 88% of all households have a television. 51% of all households have a television and a VCR. What is the probability that a household has a VCR given that it has a television? 4. A box contains 5 red balls and 9 green balls. Twoballs are drawn in succession without replacement. That is, the first ball is selected and its coloris noted but it is not replaced, then a second ball is selected. What is the probability that: a. the first ball is green and the second ball is green? b. the first ball is green and the second ball is red? c. the first ball is red and the second ball is green? d. the first ball is red and the second ball is red? 5. The probability that Sam parks in a no-parking zone and gets a parking ticketis 0.06. The probability that Sam has to park in a no-parking zone (he cannot find a legal parking space) is 0.20. Today, Sam arrives at schooland has to park in a no-parking zone. What is the probability that he will get a parking ticket? 6. An automobile dealer has kept records on the customers who visited his showroom. Forty percent of the people whovisited his dealership were women. Furthermore, his records show that 37% of the women whovisited his dealership purchased an automobile, while 21% of the men who visited his dealership purchased an automobile. a. What is the probability that a customer entering the showroom willbuy an automobile? b. Suppose a customer visited the showroomand purchased a car. Whatis the probability that the customer was a woman? c. Suppose a customer visited the showroombut did not purchase a car. What is the probability that the customer was a man? 7. Lets return to the scenario that began our discussion: A particular test correctly identifies those with a certain serious disease 94% of the time and correctly diagnoses those without the disease 98% of the time. A friend has just informed you that he has received a positive result and asks for your advice about how to interpret these probabilities. He knows nothing about probability, but he feels that because the test is quite accurate, the probability that he does have the disease is quite high, likely in the 95% range. Before attempting to address your friends concern, you research the illness and discover that 4% of men have this disease. What is the probability your friend actually has the disease? Note: For solve no. 5-7 needs the TheLaw ofTotal Probability andBayes Theorem

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Conditional probability worksheet2

  • 1. Worksheet: Probability Theory by Fachrur Rozi, M.Si CONDITIONAL PROBABILITY AND BAYES THEOREM 1. At Kennedy Middle School,the probability that a student takes Technology and Spanish is 0.087. The probability that a student takes Technology is 0.68. What is the probability that a student takes Spanish given that the student is taking Technology? 2. At a middle school,18% of all students play footballand basketball and 32% of all students play football.What is the probability that a student plays basketball given that the student plays football? 3. In Indonesia, 88% of all households have a television. 51% of all households have a television and a VCR. What is the probability that a household has a VCR given that it has a television? 4. A box contains 5 red balls and 9 green balls. Twoballs are drawn in succession without replacement. That is, the first ball is selected and its coloris noted but it is not replaced, then a second ball is selected. What is the probability that: a. the first ball is green and the second ball is green? b. the first ball is green and the second ball is red? c. the first ball is red and the second ball is green? d. the first ball is red and the second ball is red? 5. The probability that Sam parks in a no-parking zone and gets a parking ticketis 0.06. The probability that Sam has to park in a no-parking zone (he cannot find a legal parking space) is 0.20. Today, Sam arrives at schooland has to park in a no-parking zone. What is the probability that he will get a parking ticket? 6. An automobile dealer has kept records on the customers who visited his showroom. Forty percent of the people whovisited his dealership were women. Furthermore, his records show that 37% of the women whovisited his dealership purchased an automobile, while 21% of the men who visited his dealership purchased an automobile. a. What is the probability that a customer entering the showroom willbuy an automobile? b. Suppose a customer visited the showroomand purchased a car. Whatis the probability that the customer was a woman? c. Suppose a customer visited the showroombut did not purchase a car. What is the probability that the customer was a man? 7. Lets return to the scenario that began our discussion: A particular test correctly identifies those with a certain serious disease 94% of the time and correctly diagnoses those without the disease 98% of the time. A friend has just informed you that he has received a positive result and asks for your advice about how to interpret these probabilities. He knows nothing about probability, but he feels that because the test is quite accurate, the probability that he does have the disease is quite high, likely in the 95% range. Before attempting to address your friends concern, you research the illness and discover that 4% of men have this disease. What is the probability your friend actually has the disease? Note: For solve no. 5-7 needs the TheLaw ofTotal Probability andBayes Theorem