Suppose that based on symptoms a patient has, his doctor is 60% certain that the patient has a particular disease. If doctor's suspicions would be overwhelming, say at least 85%, then he would recommend a surgery. Under these circumstances, the doctor opts for quite an invasive and expensive procedure, which unfortunately is not 100% reliable. In particular, the test can show positive even if the patient does not have the disease (false positive), because of his diabetes. Chances of this is 30%. On the other hand, the test can show negative if the patient does have the disease (false negative) in 10% of all cases. Question is, in the event the test shows positive, how
Suppose that based on symptoms a patient has, his doctor is 60% certain that the patient has a
particular disease. If doctor's suspicions would be overwhelming, say at least 85%, then he would
recommend a surgery. Under these circumstances, the doctor opts for quite an invasive and
expensive procedure, which unfortunately is not 100% reliable. In particular, the test can show
positive even if the patient does not have the disease (false positive), because of his diabetes.
Chances of this is 30%. On the other hand, the test can show negative if the patient does have the
disease (false negative) in 10% of all cases. Question is, in the
much higher the prior estimate of 60% should increase to make the test worth rendering. Can we
accurately predict the results of this before running the test in order to see if a positive test will
elevate the prior from 60% to 85% or higher?
Please keep conditional probability in mind when answering this.
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