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Suppose that the reliability of a HIV test is specified as follows: Of people having HIV, 90% of the test detect the disease but 10% go undetected of
people free of HIV, 99% of the test are judged HIV –ve but 1% are diagnosed as showing HIV +ve. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV +ve. What is the probability that the person actually has HIV?
  • a)
    0.072
  • b)
    0.095
  • c)
    0.083
  • d)
    0.12
Correct answer is option 'C'. Can you explain this answer?
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Suppose that the reliability of a HIV test is specified as follows: Of...
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Suppose that the reliability of a HIV test is specified as follows: Of...
Understanding the Problem
To determine the probability that a person has HIV given a positive test result, we will use Bayes' theorem.
Definitions
- P(HIV): Probability of having HIV = 0.001 (0.1%)
- P(No HIV): Probability of not having HIV = 0.999 (99.9%)
- P(Pos | HIV): Probability of testing positive given HIV = 0.9 (90%)
- P(Pos | No HIV): Probability of testing positive given no HIV = 0.01 (1%)
Calculating the Required Probability
We need to find P(HIV | Pos), the probability of having HIV given a positive test result. According to Bayes' theorem:
P(HIV | Pos) = (P(Pos | HIV) * P(HIV)) / P(Pos)
Calculating P(Pos)
P(Pos) can be calculated as follows:
- P(Pos) = P(Pos | HIV) * P(HIV) + P(Pos | No HIV) * P(No HIV)
- P(Pos) = (0.9 * 0.001) + (0.01 * 0.999)
- P(Pos) = 0.0009 + 0.00999 = 0.01089
Final Calculation
Now substitute back into Bayes' theorem:
P(HIV | Pos) = (0.9 * 0.001) / 0.01089
P(HIV | Pos) ≈ 0.0828
This rounds to approximately 0.083, which corresponds to option 'C'.
Conclusion
Thus, the probability that a person actually has HIV given a positive test result is approximately 0.083.
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Suppose that the reliability of a HIV test is specified as follows: Of people having HIV, 90% of the test detect the disease but 10% go undetected ofpeople free of HIV, 99% of the test are judged HIV –ve but 1% are diagnosed as showing HIV +ve. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV +ve. What is the probability that the person actually has HIV?a)0.072b)0.095c) 0.083d)0.12Correct answer is option 'C'. Can you explain this answer?
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Suppose that the reliability of a HIV test is specified as follows: Of people having HIV, 90% of the test detect the disease but 10% go undetected ofpeople free of HIV, 99% of the test are judged HIV –ve but 1% are diagnosed as showing HIV +ve. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV +ve. What is the probability that the person actually has HIV?a)0.072b)0.095c) 0.083d)0.12Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Suppose that the reliability of a HIV test is specified as follows: Of people having HIV, 90% of the test detect the disease but 10% go undetected ofpeople free of HIV, 99% of the test are judged HIV –ve but 1% are diagnosed as showing HIV +ve. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV +ve. What is the probability that the person actually has HIV?a)0.072b)0.095c) 0.083d)0.12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that the reliability of a HIV test is specified as follows: Of people having HIV, 90% of the test detect the disease but 10% go undetected ofpeople free of HIV, 99% of the test are judged HIV –ve but 1% are diagnosed as showing HIV +ve. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV +ve. What is the probability that the person actually has HIV?a)0.072b)0.095c) 0.083d)0.12Correct answer is option 'C'. Can you explain this answer?.
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