Question

If the diagnostic test reports that a person chosen at random from the population has the disease, what is the conditional probability that the person, in fact, has the disease?

A) 0.01
B) 0.09
C) 0.1
D) 0.5

Answer 1

To find the conditional probability that a person chosen at random from the population has the disease given that the diagnostic test reports positive, we need to use Bayes' theorem.

Step-by-step explanation:

To find the conditional probability that a person chosen at random from the population has the disease given that the diagnostic test reports positive, we need to use Bayes' theorem. Let's denote the following:

• A: Event that the person has the disease
• B: Event that the diagnostic test reports positive

We are given:

• P(A) = 3059/100000 (total cases of the disease in the population)
• P(B|A) = 1 (the test reports positive when the person has the disease)
• P(B) = ? (probability that the test reports positive)

According to Bayes' theorem, the conditional probability that the person has the disease given that the test reports positive is:

P(A|B) = (P(B|A) * P(A)) / P(B)

Substituting the given values:

P(A|B) = (1 * 3059/100000) / P(B)

To find P(B), we would need additional information about the test's accuracy (e.g., false positive rate and false negative rate).