Consider the problem of diagnosing a rare disease. Let’s say the occurrence of this disease is one in a thousand i.e. P(D = +) = 0.001. There is a test T which correctly identifies the disease 99.9% of the time, i.e. P(T = +|D = +) = 0.999. However, it also has a false positive rate of 0.02, i.e. P(T = +|D = −) = 0.02 i. If a random person from the population is tested, what is the probability they will receive a positive test, i.e. P(T = +)? ii. Given that the test is positive, what is the probability that the person has the disease, i.e. P(D = +|T = +)?
Consider the problem of diagnosing a rare disease. Let’s say the occurrence of this disease is one in a thousand i.e. P(D = +) = 0.001. There is a test T which correctly identifies the disease 99.9% of the time, i.e. P(T = +|D = +) = 0.999. However, it also has a false positive rate of 0.02, i.e. P(T = +|D = −) = 0.02 i. If a random person from the population is tested, what is the probability they will receive a positive test, i.e. P(T = +)? ii. Given that the test is positive, what is the probability that the person has the disease, i.e. P(D = +|T = +)?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider the problem of diagnosing a rare disease. Let’s say the occurrence of this
disease is one in a thousand i.e. P(D = +) = 0.001. There is a test T which correctly
identifies the disease 99.9% of the time, i.e. P(T = +|D = +) = 0.999. However, it
also has a false positive rate of 0.02, i.e. P(T = +|D = −) = 0.02
i. If a random person from the population is tested, what is the probability they will
receive a positive test, i.e. P(T = +)?
ii. Given that the test is positive, what is the probability that the person has the disease,
i.e. P(D = +|T = +)?
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