Question

A certain disease has an incidence rate of 0.1%. if the false negative rate is 4% and the false positive rate is 1%, compute the probability that a person who tests positive actually has the disease. write the probability as a decimal rounded to three decimal places.

Answer 1

To compute the probability that a person who tests positive actually has the disease, we can use Bayes' theorem. Plugging in the values, we find that the probability is approximately 0.091.

Step-by-step explanation:

To compute the probability that a person who tests positive actually has the disease, we need to use Bayes' theorem.

Let:
P(D) be the probability that a person has the disease = 0.001 (0.1% incidence rate)
P(FN) be the probability of a false negative = 0.04 (4% false negative rate)
P(FP) be the probability of a false positive = 0.01 (1% false positive rate)
P(Pos) be the probability of testing positive

We can calculate P(Pos|D), the probability of testing positive given the person has the disease, using the formula:

P(Pos|D) = (P(D) * (1 - P(FN))) / ((P(D) * (1 - P(FN))) + ((1 - P(D)) * P(FP)))

Plugging in the values, we get:

P(Pos|D) = (0.001 * (1 - 0.04)) / ((0.001 * (1 - 0.04)) + ((1 - 0.001) * 0.01))

Calculating the fraction and rounding to three decimal places, we find that the probability that a person who tests positive actually has the disease is approximately 0.091.