A pharmaceutical company has developed a nearly accurate test for the disease A.

Question

A pharmaceutical company has developed a nearly accurate test for the disease A. The accuracy of the test is 99%, that is, with probability 0.99 it gives the correct result (the same probability for disease-positive-test and no-disease-negative-test combinations are assumed) and only in 1% of tested cases probability 0.01) the result is wrong. The incidence of the disease in the population is 0.01% (probability 0.0001). Compute the probability that somebody from wide population who has tested positive indeed suffers from the disease. Would you recommend the test to be widely adopted?

Explanation / Answer

here probabilty of tested postive =0.0001*0.99+0.9999*0.01=0.010098

hence probability of suffering from disease given tested positive =0.0001*0.99/0.010098=0.009804

as probabilty of above is very less we should not advise it to be widely adopted

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