Example 18 - Suppose reliability of a HIV test is: people - Bayes theoram

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  1. Chapter 13 Class 12 Probability
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Transcript

Example 18 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 ive but 1% are diagnosed as showing HIV +ive. 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 + ive. What is the probability that the person actually has HIV? Let E : person selected has HIV F : person selected does not have HIV G: test judges HIV +ve We need to find the Probability that the person selected actually has HIV, if the test judges HIV +ve i.e. P(E|G) P(E|G) = . ( | ) . | + . ( | ) Putting values in formula, P(E|G) = 0.001 0.9 0.001 0.9 + 0.999 0.01 = 9 10 4 9 10 4 + 99.9 10 4 = 10 4 9 10 4 [9 + 99.9] = 9 108.9 = = 0.083 (approx) Therefore, required probability is 0.083

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