Only 0.1% of the individuals in a certain population have a particular disease (an incidence rate of .001). Of those who have the disease, 90% test positive when a certain diagnostic test is applied. Of those who do not have the disease, 90% test negative when the test is applied. Suppose that an individual from this population is randomly selected and given the test. Use the general multiplication rule to calculate P (has disease AND positive test) and P (no disease AND positive test). Calculate P (positive test) and P (negative test). Calculate P (has disease | positive test). Does the result surprise you? Give an intuitive explanation for why this probability is small.

Only 0.1% of the individuals in a certain population have a particular disease (an incidence rate of .001). Of those who have the disease, 90% test positive when a certain diagnostic test is applied. Of those who do not have the disease, 90% test negative when the test is applied. Suppose that an individual from this population is randomly selected and given the test. Use the general multiplication rule to calculate P (has disease AND positive test) and P (no disease AND positive test). Calculate P (positive test) and P (negative test). Calculate P (has disease | positive test). Does the result surprise you? Give an intuitive explanation for why this probability is small.

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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Use the general multiplication rule to calculate P (has disease AND positive test) and P (no disease AND positive test).
Calculate P (positive test) and P (negative test).
Calculate P (has disease | positive test). Does the result surprise you? Give an intuitive explanation for why this probability is small.

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