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Math Help - Probability of a disease test

  1. #1
    kin
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    Probability of a disease test

    Suppose that there is a blood test for a particular disease.
    The probability of giving positive result at the presence of the diseae is 85%,
    while the probability of giving negative result at the absence of the disease is 95%.

    Accordng to the previous experience, 7% of the patients who have undergone the test have that disease.

    a) What's the probability that the patient has the disease if the test gives positive result?

    b) Suppose that the patient has taken the test twice. The 2 tests are taken in two labs seperately under similar lab conditions.
    What's probability that the patient has the disease both tests give positive results?
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    Quote Originally Posted by kin View Post
    Suppose that there is a blood test for a particular disease.
    The probability of giving positive result at the presence of the diseae is 85%,
    while the probability of giving negative result at the absence of the disease is 95%.

    Accordng to the previous experience, 7% of the patients who have undergone the test have that disease.

    a) What's the probability that the patient has the disease if the test gives positive result?

    b) Suppose that the patient has taken the test twice. The 2 tests are taken in two labs seperately under similar lab conditions.
    What's probability that the patient has the disease both tests give positive results?
    Pr(+ve | D) = 0.85.
    Pr(-ve | D') = 0.95.
    Pr(D) = 0.07.

    I drew a tree diagram.

    a) From the tree diagram: \Pr(D \, | \, +ve) = \frac{(0.07)(0.85)}{(0.07)(0.85) + (0.93)(0.05)}.
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