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Probability Problems chapter 15 part 2 General addition rule Testing for independence Tree diagram

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Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% a blood test, and 22% both. What is the probability that a randomly selected DWI suspect is given: (use a venn diagram for general addition rule) 1- a test? 2- a blood or breath test but not both? 3- neither? (use a table) 4- Are giving a blood and breath test mutually exclusive? 5- Are giving the two tests independent?

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Blood TestBreath Test Both tests No Test 22%56%14% 8%

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Blood Test Breath Test Both tests No Test 22%56%14% What is the probability that a randomly selected DWI suspect is given: 1- a test? 2- a blood or breath test but not both? 3- neither? 8%

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Blood Test Breath Test Both tests No Test 22%56%14% 8% YESNOTOTALS YES NO TOTALS BREATH TEST BLOOD TEST

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YESNOTOTALS YES0.220.140.36 NO0.560.080.64 TOTALS0.780.221.00 BREATH TEST BLOOD TEST What is the probability that a randomly selected DWI suspect is given: 4- Are giving a blood and breath test mutually exclusive (DISJOINT)? 5- Are giving the two tests independent?

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A TB test is 99% accurate. If the incidence of having TB in the US is 5 in 100,000 or 0.00005 and the probability of having a false negative test is 0.001. What is the probability of actually having TB if you test positive for it?

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-P (+ | TB) = 0.99 -P(TB in the US) = 0.00005 -P( - | TB) = 0.001 -What is the probability of actually having TB if you test positive for it?

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