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5 to reduce laboratory costs water samples from three

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5.To reduce laboratory costs, water samples from three public swimming pools are combined forone test for the presence of bacteria. Further testing is done only if the combined sample testspositive. Based on past results, there is a 0.009 probability of finding bacteria in a publicswimming area. Find the probability that a combined sample from three public swimmingareas will reveal the presence of bacteria. Is the probability low enough so that further testingof the individual samples is rarely necessary?
b.Is the probability low enough so that further testing of the individual samples is rarelynecessary?
6.Explain how to read the notation P(E|F).
7.Let event A = subject is telling the truth and event B = polygraph test indicates that the subjectis lying. Use your own words to translate the notation P( B|A )into a verbal statement.
8.The conditional probability of B given A can be found by _______.
9.The data represent the results for a test for a certain disease. Assume one individual from thegroup is randomly selected. Find the probability of getting someone who tests negative, giventhat he or she did not have the disease.The individual actually had the diseaseYesNoPositive13418Negative10138a.The probability is approximately 0.885
10.The table below displays results from experiments with polygraph instruments. Find thepositive predictive value for the test. That is, find the probability that the subject lied, giventhat the test yields a positive result.Did the subject actually lie?No (did not lie)Yes (did lie)Positive test results1840Negative test results3412a.The probability is0.69(Round to three decimal places as needed.)
11..
12.The probability that a randomly selected adult in a particular community is a smoker is 18%.The probability that a randomly selected adult in the community is a smoker, given that theadult earns more than $75,000 per year, is 18%. Are the events "is a smoker" and "earns morethan $75,000 per year" independent? Explain.
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Term
Summer
Professor
KISHBAUGH,GRETA
Tags
Management, Conditional Probability, Probability, Probability theory, Restaurant A

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