Suppose that a test for a disease is such that it is 98% accurate in the case wh

Question

Suppose that a test for a disease is such that it is 98% accurate in the case when the person actually has the disease and 97% accurate in giving a negative result in the case when the person does not have the disease. Suppose it is known that 1% of the entire population has this disease. You test someone and they test positive. What is the probability that they have the disease? Suppose that a test for a disease is such that it is 98% accurate in the case when the person actually has the disease and 97% accurate in giving a negative result in the case when the person does not have the disease. Suppose it is known that 1% of the entire population has this disease. You test someone and they test positive. What is the probability that they have the disease? Suppose that a test for a disease is such that it is 98% accurate in the case when the person actually has the disease and 97% accurate in giving a negative result in the case when the person does not have the disease. Suppose it is known that 1% of the entire population has this disease. You test someone and they test positive. What is the probability that they have the disease?

Explanation / Answer

probability of test postive =P(T+) =P(have disease and test postive+not have disease and test posiitve)

=0.01*0.98+(1-0.01)*(1-0.97)=0.0395=0.0395

hence probability that they have the disease given test positive

=P(have disease and test postive)/P(test positive) =0.01*0.98/0.0395=0.2481

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