Use Bayes' theorem to find the indicated probability.
-3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have
The disease also test positive (false positives). A person is randomly selected and tested for the disease. What is
The probability that the person has the disease given that the test result is positive?
A) 0.038
B) 0.475
C) 0.525
D) 0.905

Question

Quizplus · Accepted Answer

P(Disease|Positive) = P(Positive|Disease) * P(Disease) / P(Positive)P(Positive|Disease) = 0.939P(Disease) = 0.038P(Positive) = P(Positive|Disease) * P(Disease) + P(Positive|No Disease) * P(No Disease)P(Positive) = 0.939 * 0.038 + 0.041 * (1 - 0.038)P(Positive) = 0.036 + 0.039P(Positive) = 0.075P(Disease|Positive) = 0.939 * 0.038 / 0.075P(Disease|Positive) = 0.475

Use Bayes' Theorem to Find the Indicated Probability