Homework Help is Here – Start Your Trial Now!
Math
Probability
Suppose we are studying a test for a rare disease which is present in .5% of people (probability .005). If a person has the disease, the test will detect it 90% of the time (true positive rate). If a person does not have the disease, the test will detect it 95% of the time (true negative rate). (a) What is the probability that a person with a positive test result has the disease? (b) How high does the true negative rate have to be before the probability in part (a) is ? (c) Repeat parts (a) and (b), but assume the disease is much more common, and is present in 10% of people.

Suppose we are studying a test for a rare disease which is present in .5% of people (probability .005). If a person has the disease, the test will detect it 90% of the time (true positive rate). If a person does not have the disease, the test will detect it 95% of the time (true negative rate). (a) What is the probability that a person with a positive test result has the disease? (b) How high does the true negative rate have to be before the probability in part (a) is ? (c) Repeat parts (a) and (b), but assume the disease is much more common, and is present in 10% of people.

A First Course in Probability (10th Edition)
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...
See similar textbooks
icon
Related questions
Question

This is an easy question

Suppose we are studying a test for a rare disease which is present in .5% of people (probability .005). If a person has the disease, the test will detect it 90% of the time (true positive rate). If a person does not have the disease, the test will detect it 95% of the time (true negative rate). (a) What is the probability that a person with a positive test result has the disease? (b) How high does the true negative rate have to be before the probability in part (a) is ? (c) Repeat parts (a) and (b), but assume the disease is much more common, and is present in 10% of people.
Transcribed Image Text:Suppose we are studying a test for a rare disease which is present in .5% of people (probability .005). If a person has the disease, the test will detect it 90% of the time (true positive rate). If a person does not have the disease, the test will detect it 95% of the time (true negative rate). (a) What is the probability that a person with a positive test result has the disease? (b) How high does the true negative rate have to be before the probability in part (a) is ? (c) Repeat parts (a) and (b), but assume the disease is much more common, and is present in 10% of people.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer