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A certain disease has an incidence rate of 0.5%_ If the false negative rate is 4% and the false positive rate is 5%, compute the probability that person who tests p...

Question

A certain disease has an incidence rate of 0.5%_ If the false negative rate is 4% and the false positive rate is 5%, compute the probability that person who tests positive actually has the disease. Give your answer accurate to at least 3 decimal places Check Answer

A certain disease has an incidence rate of 0.5%_ If the false negative rate is 4% and the false positive rate is 5%, compute the probability that person who tests positive actually has the disease. Give your answer accurate to at least 3 decimal places Check Answer



Answers

A test for the presence of a disease has probability 20 of giving a false-positive reading (indicating that an individual has the disease when this is not the case) and probability. 10 of giving a false-negative result. Suppose that ten individuals are tested, five of whom have the disease and five of whom do not. Let $X=$ the number of positive readings that result.
(a) Does $X$ have a binomial distribution? Explain your reasoning.
(b) What is the probability that exactly three of the ten test results are positive?


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