Hello, JP101!

We need Bayes' Theorem: .

Suppose 30% of the individuals in a community are infected with a dreaded virus.

Of those with the virus, 5% test negative for the disease

and 95% of those who do not have the virus test negative for the disease.

Find the probability that a person has the virus, given they tested negative for it.

We are given: .

Also: .

We want: . .(a)

Using Bayes' Theorem, [3] becomes: .

Substituting [1], we have: . .[5]

Using Bayes' Theorem, [4] becomes: .

Substituting [2], we have: . .[6]

Combining [5] and [6]: .

Substitute into (a): .