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In a certain population, 1% of all individuals are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for non-carriers that the diagnostic test is applied independently to two different samples from the same randomly selected individual.   What is the probability that both tests yield the same results?

In a certain population, 1% of all individuals are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for non-carriers that the diagnostic test is applied independently to two different samples from the same randomly selected individual.   What is the probability that both tests yield the same results?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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  1. In a certain population, 1% of all individuals are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for non-carriers that the diagnostic test is applied independently to two different samples from the same randomly selected individual.

 

  • What is the probability that both tests yield the same results?

 

 

 

 

 

 

 

 

 

 

 If both tests are positive, what is the probability that the selected individual is a carrier?

Expert Solution
Step 1: Given information

In a certain population, 1 percent sign of all individuals are carriers of a particular disease.

A diagnostic test for this disease has the following detection rates:

  • 90 percent sign detection rate for carriers (sensitivity).
  • 5 percent sign detection rate for non-carriers (specificity).

The diagnostic test is applied independently to two different samples from the same randomly selected individual.

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