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Imagine a population in the midst of an epidemic where 60% of the population is considered...

Imagine a population in the midst of an epidemic where 60% of the population is considered susceptible, 10% are infected, and 30% are recovered. There is only one test for the disease. For susceptible patients the test is accurate (i.e. returns a negative result) 95% of the time. For infected patients the test is correct (i.e. returns a positive result) 99% of the time. The test is correct (i.e. returns a negative results) 65% of the time for recovered individuals.

a) Find the probability a patient actually is infected given they received a positive test result. Circle your final answer. Hint: It may be helpful to draw a tree diagram.

b) Are the events of “being susceptible” and “having a positive test result” independent?

Math   Statistics-And-Probability   
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