1.8% of a population are infected with a certain disease.There is a test for the disease,however the test is not completely accurate.94.2% of those who have the disease will test positive.However 4.8% of those who do not have the disease will also test positive (false positives).What is the probability that a person who tests positive actually has the disease?
A)0.360
B)0.265
C)0.942
D)0.018
E)0.735

Question

Quizplus · Accepted Answer

Let's use Bayes' theorem to solve this problem:
P(disease|positive) = P(positive|disease) * P(disease) / P(positive)
P(disease|positive) = 0.942 * 0.018 / (0.942 * 0.018 + 0.048 * 0.982)
P(disease|positive) = 0.265
Therefore, the probability that a person who tests positive actually has the disease is 0.265, which corresponds to choice B.

18% of a Population Are Infected with a Certain Disease