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3.9% of a secluded island tribe are infected with a certain disease. There is a test...

3.9% of a secluded island tribe are infected with a certain disease. There is a test for the​ disease, however the test is not completely accurate.​ 92% of those who have the disease will test positive. However​ 4.4% of those who do not have the disease will also test positive​ (false positives). Use a tree diagram to find the probability that any given person will test positive. Round your answer to three decimal places if necessary.

Math   Statistics-And-Probability   
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Answer #1

P[ Person will test positive ] = P[ Person has disease ]*P[ Test is positive | person has disease ] + P[ Person do not has disease ]*P[ Test is positive | person do not has disease ]

P[ Person will test positive ] = 0.039*0.92 + 0.961*0.044

P[ Person will test positive ] = 0.03588 + 0.042284

P[ Person will test positive ] = 0.078164

P[ Person will test positive ] = 7.8%

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