A rare disease is present in 1 of the population Suppose tha

A rare disease is present in 1% of the population. Suppose that a test for the disease is positive 99% of the time when an individual has the disease and 5% of the time when the individual does not have the disease.

A. What is the probability that an individual tests negative given the disease is present?

Solution

here it is given that 1% of population have the disease

and 99% the test is positive when the the disease is present

which means 1% it is negative even the disease it present

hence there is 1% chances that the individual will test negative even after having the disease.

probability = 1%*1% = 0.01*0.01 = 0.0001 ( as 1% of population only have disease)