A diagnostic test has a probability of 92% of giving a positive result when applied to...

A diagnostic test has a probability of 92% of giving a positive result when applied to a person suffering from a certain disease. The test has a probability of 5% of giving a false positive when applied to a non-sufferer. If 6% of the population suffer from the disease, what is the probability of a positive test result?

Expert Solution

Solution

Let's define

P(S) = Probability of suffering of population from disease

P(NS) = Probability of Non suffering of Population from disease

P(P/S) = Probability of getting positive when suffering

P(P/NS) = Probability of getting positive when Non suffering

In this problem,

We have used the Total Probability Theorem stated below

P(P) = P(S) *P(P/S) + P(NS) *P(P/NS)

Please see the attached file

orchestra answered 2 years ago

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