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10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is _________.
Correct answer is between '0.48,0.49'. Can you explain this answer?
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10% of the population in a town is HIV+. A new diagnostic kit for HIV ...
Let total population = 100
HIV + patients = 10
For the patient to be +Ve, should be either +VE and test is showing the or the patient
should be – Ve but rest is showing +Ve
should be – Ve but rest is showing +Ve
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10% of the population in a town is HIV+. A new diagnostic kit for HIV ...
Negative individuals 98% of the time.
To calculate the probability of a randomly selected individual having HIV given that they tested positive with the diagnostic kit, we can use Bayes' theorem.
Let's assume the population of the town is 1000 individuals.
The number of individuals with HIV in the town would be 10% of 1000, which is 100.
Out of these 100 HIV positive individuals, the diagnostic kit correctly identifies 95% of them, which means it gives a true positive result for 95 individuals.
Now, out of the 900 HIV negative individuals in the town, the diagnostic kit incorrectly identifies 2% of them as false positives, which means it gives a positive result for 2% of 900, which is 18 individuals.
Therefore, the total number of individuals who tested positive with the diagnostic kit is 95 (HIV positive individuals) + 18 (false positive individuals) = 113.
Now, to calculate the probability of a randomly selected individual having HIV given that they tested positive with the diagnostic kit, we use Bayes' theorem:
P(HIV | positive result) = (P(positive result | HIV) * P(HIV)) / P(positive result)
P(HIV | positive result) = (95/113) * (100/1000) / (113/1000)
P(HIV | positive result) ≈ 0.8416
Therefore, the probability of a randomly selected individual having HIV given that they tested positive with the diagnostic kit is approximately 0.8416 or 84.16%.
To calculate the probability of a randomly selected individual having HIV given that they tested positive with the diagnostic kit, we can use Bayes' theorem.
Let's assume the population of the town is 1000 individuals.
The number of individuals with HIV in the town would be 10% of 1000, which is 100.
Out of these 100 HIV positive individuals, the diagnostic kit correctly identifies 95% of them, which means it gives a true positive result for 95 individuals.
Now, out of the 900 HIV negative individuals in the town, the diagnostic kit incorrectly identifies 2% of them as false positives, which means it gives a positive result for 2% of 900, which is 18 individuals.
Therefore, the total number of individuals who tested positive with the diagnostic kit is 95 (HIV positive individuals) + 18 (false positive individuals) = 113.
Now, to calculate the probability of a randomly selected individual having HIV given that they tested positive with the diagnostic kit, we use Bayes' theorem:
P(HIV | positive result) = (P(positive result | HIV) * P(HIV)) / P(positive result)
P(HIV | positive result) = (95/113) * (100/1000) / (113/1000)
P(HIV | positive result) ≈ 0.8416
Therefore, the probability of a randomly selected individual having HIV given that they tested positive with the diagnostic kit is approximately 0.8416 or 84.16%.
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10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available;this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. Theprobability that the individual is actually positive is _________.Correct answer is between '0.48,0.49'. Can you explain this answer?
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10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available;this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. Theprobability that the individual is actually positive is _________.Correct answer is between '0.48,0.49'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available;this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. Theprobability that the individual is actually positive is _________.Correct answer is between '0.48,0.49'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available;this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. Theprobability that the individual is actually positive is _________.Correct answer is between '0.48,0.49'. Can you explain this answer?.
10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available;this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. Theprobability that the individual is actually positive is _________.Correct answer is between '0.48,0.49'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available;this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. Theprobability that the individual is actually positive is _________.Correct answer is between '0.48,0.49'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available;this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. Theprobability that the individual is actually positive is _________.Correct answer is between '0.48,0.49'. Can you explain this answer?.
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