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In a certain population, 1% of all individuals are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for non- carriers. Suppose that the diagnostic test is applied independently to two different samples from the same randomly selected individual.
a) What is the probability that both test yield the same result?
B) If both tests are positive, what is the probability that the selected individual is a carrier?

i have no idea on where to start.

  • statistics -

    Excel spreadsheets are very helpful for these kinds of problems.

    Start by building a probability tree, calculate all possible values. There are 2 kinds of people (with and without), and each test has two answers (yes, no). So, there should be 8 possible outcomes.
    The probability of seeing a person with the disease and both test positive is: .01*.9*.9 = .0081
    of seeing a person with the disease and the first test is positive and the second negative = .01*.9*.1 = .0009
    Repeat for the other 6 possibilities. If you did the calculations right, the sum of the 8 values should be 1.0.

    Then you will have all the information you need.

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