Assume there is a medical test to diagnose a disease. If a person has the diseas
ID: 3045961 • Letter: A
Question
Assume there is a medical test to diagnose a disease. If a person has the disease, the probability is 95 percent that he/she will have a positive test result for the disease. If a person does not have the disease, the probability is 0.1 percent that he/she will still have a positive test result. The probability that a person has a disease is 0.5 percent in the population.
Answer the following questions:
Imagine a person who has a positive test result. What is the probability that he/she actually has the disease?
Imagine a person who has a negative test result. What is the probability that he/she actually doesn’t have the disease?
If a person has a positive test result, what is the probability that s/he doesn’t have the disease?
If a person has a negative test result, what is the probability that s/he has the disease?
Explanation / Answer
P(positive) = 0.95 * 0.005 + 0.001 * 0.995 = 0.0057
A) P(has disease | positive) = P(positive | has disease) * P(has disease)/P(positive)
= 0.95 * 0.005/0.0057 = 0.83
B) P(doesn't have the disease | negative test) = P(negative | doesn't have the disease) * P(doesn't have the disease) /P(negative) = 0.999 * 0.995/0.9943 = 0.9997
C) P(doesn't have disease | positive) = P(positive | doesn't have the disease) * P(doesn't have the disease)/P(positive) =0.001 * 0.995/0.0057 = 0.175
D) P(has the disease | negative) = P(negative | has the disease) * P(has the disease)/P(negative)
= 0.05 * 0.005/0.9943 = 0.0003