A medical test gives a correct result 90% of the time for infected individuals and 95% of the time for non-infected individuals. All members of the population are tested. The probability that a person is infected given they have a positive test result is 0.6. What proportion of the population is infected?

The proportion of the population which is infected is   =0.07692

Step-by-step explanation:

Let the events be,

A: a person is infected.

B:   the test result is positve

According to the question we have,

So

Hence,

Now

The probability that a person is infected is  

So the probability that a person is infected is =0.07692.

The proportion of the population which is infected is  

Hence the proportion of the population which is infected is   =0.07692