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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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In this chapter we look at some general rules about probability and some special diagrams that will aid us in using these rules correctly.

In this chapter we look at some general rules about probability and some special diagrams that will aid us in using these rules correctly.

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