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Given that a person has a positive test, find the probability that this person actually has cancer.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Assume that a type of cancer has a 1% prevalence rate, meaning that 1% of the population has this type of cancer. For a test developed for this type of cancer, the false positive rate is 10%. That is, the probability of a positive test result in a person who does not have cancer is 10%. The true positive rate of the test is 80%. That is, in patients with cancer the test is positive in 80% of the cases.

Given that a person has a positive test, find the probability that this person actually has cancer.

A = test was positive

B = person has cancer

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