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3. You are diagnosed with an uncommon disease. You know that among the general population there is a 3% chance of getting it. Use the letter D for the event "you have the disease" and T for the "the test says so." It is known that the test is imperfect: Pr(T|D) = 0.90 and Pr(TC | DC) = 0.95. (a) Given that you test positive (the test is positive if you have the disease), what is the probability that you really have the disease?

3. You are diagnosed with an uncommon disease. You know that among the general population there is a 3% chance of getting it. Use the letter D for the event "you have the disease" and T for the "the test says so." It is known that the test is imperfect: Pr(T|D) = 0.90 and Pr(TC | DC) = 0.95. (a) Given that you test positive (the test is positive if you have the disease), what is the probability that you really have the disease?

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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3. You are diagnosed with an uncommon disease. You know that among the general population there is a 3% chance of getting it. Use the letter D for the event "you have the disease" and T for the "the test says so." It is known that the test is imperfect: Pr(T|D) = 0.90 and Pr(TC | DC) = 0.95. (a) Given that you test positive (the test is positive if you have the disease), what is the probability that you really have the disease? (b) Suppose that after testing positive for the disease, you obtain a second opinion: an independent repetition of a test with the same overall values for true and false positives. You test positive again. Let S be the event that "you test positive again." Given this, what is the probability that you really have the disease?
Transcribed Image Text:3. You are diagnosed with an uncommon disease. You know that among the general population there is a 3% chance of getting it. Use the letter D for the event "you have the disease" and T for the "the test says so." It is known that the test is imperfect: Pr(T|D) = 0.90 and Pr(TC | DC) = 0.95. (a) Given that you test positive (the test is positive if you have the disease), what is the probability that you really have the disease? (b) Suppose that after testing positive for the disease, you obtain a second opinion: an independent repetition of a test with the same overall values for true and false positives. You test positive again. Let S be the event that "you test positive again." Given this, what is the probability that you really have the disease?
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