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Math Help - binomial issue!

  1. #1
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    binomial issue!

    the chances that doctor A will diagnose X disease correctly is 60%. the chances that a patient will die by his treatment after correct diagnose is 40% and the chances of death by wrong diagnose is 70%. a patient of doctor A, who had disease X died. what is the chances that his disease was diagnose correctly?

    pls help!
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  2. #2
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    Re: binomial issue!

    Let A be the probability that a patient will die, and B_X the probability that that the doctor will diagnose the disease X correctly.

    What you're looking for is the probability P(B_X|A)=\frac{P(A|B_X)P(B_X)}{P(A|B_X)P(B_X) + P(A|B^*_X)P(B^*_X)}

    All the probabilities needed are directly given in the text.
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  3. #3
    Newbie Flatiron's Avatar
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    Re: binomial issue!

    I always lay out problems like this with a tree (rather than using the equation from Bayes' Theorem, which always looks more complex than it really is).
    First node is "correct diagnosis"/"incorrect diagnosis."
    Second node (at the end of each branch from first node) is "die" / "don't die."
    Two paths lead to die:
    1. correct diagnosis + die, with probability 0.6 x 0.4
    2. incorrect diagnosis + die, with probability 0.4 x 0.7
    Probability of correct diagnosis is 0.24/0.52.
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