A laboratory blood test is 99% effective in detecting a certain disease when its infection is present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1% of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

Explanation

Let, the events that a person has a disease and a person has no disease be denoted by `A` and `B` respectively.

It is given that,

`P(A)=0.1%`

i.e., `P(A)=0.001`

Now, as we know that the events `A` and `B` are complementary to each other.

Therefore, `P(A)+P(B)=1`

`=>P(B)=1-P(A)`

`=>P(B)=1-0.001`

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