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A certain medical test has the following reliability: if a person has cooties the test will show positive with probability 0.95. If a person does not have cooties, the test will show negative with probability 0.6. Overall, 10% of the population has cooties. Give your answers as percentages with two decimal digits, e.g. 93.42%.
What is the probability that a randomly selected person from the population tests negative?
What is the probability that a randomly selected person from the population tests positive?
If a person tests negative, what is the probability that the person is actually free of the disease?
If a person tests positive, what is the probability that the person actually has the disease?