A screening test for a certain disease is prone to giving false positives or fal

Question

A screening test for a certain disease is prone to giving false positives or false negatives. If a patient being tested has the disease, the probability that the test indicates a (false) negative is 0.14. If the patient does not have the disease, the probability that the test indicates a (false) positive. Is 0.08. Assume that 3% of the patients being tested actually have the disease. Suppose that one patient is chosen at random and tested. Find the probability that

This patient has the disease and test positive?

The patient does not have the disease and tests positive?

This patient tests positive?

The patient has the disease given that he or she tests positive?

Explanation / Answer

given

If a patient being tested has the disease, the probability that the test indicates a (false) negative is 0.14

if the patient does not have the disease, the probability that the test indicates a (false) positive. Is 0.08.

a) This patient has the disease and test positive 0.03*.(1-0.14) = 0.0258
b).The patient does not have the disease and tests positive 0. 97*0.08= 0.0776
c) This patient tests positive 0.0258+0.0776 = 0.1034
d)   The patient has the disease given that he or she tests positive 0.0258/0.1034 = 0.2495

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