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6. A rare genetic disease is discovered. Although only one in a million people carry it, you consider getting screened. You are told that the genetic test is extremely good; it is 100% sensitive (it is always correct if you have the disease) and 99.99% specific (it gives a false positive result only 0.01% of the time). Having recently learned Bayes' theorem, you decide not to take the test. Why? Basically, find the probability of being healthy given the positive test (PT) and tell me would you have the test done? Answer: P(Healthy given Positive Test) = Would you have the test done and why?

6. A rare genetic disease is discovered. Although only one in a million people carry it, you consider getting screened. You are told that the genetic test is extremely good; it is 100% sensitive (it is always correct if you have the disease) and 99.99% specific (it gives a false positive result only 0.01% of the time). Having recently learned Bayes' theorem, you decide not to take the test. Why? Basically, find the probability of being healthy given the positive test (PT) and tell me would you have the test done? Answer: P(Healthy given Positive Test) = Would you have the test done and why?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Understanding Rare Genetic Diseases: A Bayesian Approach to Decision Making **Question 6:** A rare genetic disease is discovered. Although only one in a million people carry it, you consider getting screened. You are told that the genetic test is extremely good; it is 100% sensitive (it is always correct if you have the disease) and 99.99% specific (it gives a false positive result only 0.01% of the time). Having recently learned Bayes' theorem, you decide not to take the test. Why? Basically, find the probability of being healthy given the positive test (PT) and tell me would you have the test done? **Answer:** P(Healthy given Positive Test) = _______________ Would you have the test done and why? ____________________________ _________________________________________ _________________________________________ At the bottom of the document, there is a visual representation of Bayes' theorem application: \[ P(\text{Healthy} \mid \text{Positive Test}) = \frac{P(\text{Healthy}) \cdot P(\text{Positive Test} \mid \text{Healthy})}{P(\text{Positive Test})} = \frac{1}{0.01} \] This exercise illustrates the importance of considering both the sensitivity and specificity of medical tests in relation to the prevalence of the disease when making decisions based on test outcomes.
Transcribed Image Text:### Understanding Rare Genetic Diseases: A Bayesian Approach to Decision Making **Question 6:** A rare genetic disease is discovered. Although only one in a million people carry it, you consider getting screened. You are told that the genetic test is extremely good; it is 100% sensitive (it is always correct if you have the disease) and 99.99% specific (it gives a false positive result only 0.01% of the time). Having recently learned Bayes' theorem, you decide not to take the test. Why? Basically, find the probability of being healthy given the positive test (PT) and tell me would you have the test done? **Answer:** P(Healthy given Positive Test) = _______________ Would you have the test done and why? ____________________________ _________________________________________ _________________________________________ At the bottom of the document, there is a visual representation of Bayes' theorem application: \[ P(\text{Healthy} \mid \text{Positive Test}) = \frac{P(\text{Healthy}) \cdot P(\text{Positive Test} \mid \text{Healthy})}{P(\text{Positive Test})} = \frac{1}{0.01} \] This exercise illustrates the importance of considering both the sensitivity and specificity of medical tests in relation to the prevalence of the disease when making decisions based on test outcomes.
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