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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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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.
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