Question

Assume that 0.4% of the population has a condition that is not detectible by simple external observation. A diagnostic test is available for this condition, but, like most tests, it is not perfect. The test correctly diagnoses, with a positive result, those with the condition 99.7% of the time. The test correctly identifies, with a negative result, those without the condition 98.5% of the time.

1. Let the event C₁ represent the presence of the condition and C₂ represent the absence of the condition, and let event T represent a positive test result (meaning the test indicated, either correctly or incorrectly, that a person has the condition) and T^C represent a negative test result (meaning the test indicated, either correctly or incorrectly, that a person does not have the condition). List symbolically the information given in the introductory statement at the top of the page.

                            

2. If a randomly selected member of the population tests positive for the condition, what is the probability that the person has the condition? (Report or round your answer to 3 decimal places.)

                      Find:

                      Formula(s):

                      Computations:

                      Answer:

3. If a randomly selected member of the population tests positive for the condition, what is the probability that the person does not have the condition?

4. If a randomly selected member of the population tests negative for the condition, what is the probability that the person has the condition? (Report or round your answer to 6 decimal places.)

   Assume that 0.4% of the population has a condition that is not detectible by simple external observation. A diagnostic test is available for this condition, but, like most tests, it is not perfect. The test correctly diagnoses, with a positive result, those with the condition 99.7% of the time. The test correctly identifies, with a negative result, those without the condition 98.5% of the time.

5. Let the event C₁ represent the presence of the condition and C₂ represent the absence of the condition, and let event T represent a positive test result (meaning the test indicated, either correctly or incorrectly, that a person has the condition) and T^C represent a negative test result (meaning the test indicated, either correctly or incorrectly, that a person does not have the condition). List symbolically the information given in the introductory statement at the top of the page.

6.                             

7. If a randomly selected member of the population tests positive for the condition, what is the probability that the person has the condition? (Report or round your answer to 3 decimal places.)

8.                       Find:

                         Formula(s):

                         Computations:

                         Answer:

9. If a randomly selected member of the population tests positive for the condition, what is the probability that the person does not have the condition?
10. If a randomly selected member of the population tests negative for the condition, what is the probability that the person has the condition? (Report or round your answer to 6 decimal places.)

Answer 1