Most medical tests are not completely accurate. For example, a microscopy test f
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Question
Most medical tests are not completely accurate. For example, a microscopy test for TB comes out positive with probability 0.01 when the tested individual doesn't actually have TB, and it comes out negative with probability 0.2 when the tested individual does have TB. Find the probability that a randomly chosen individual will test positive under the following conditions. (a) The frequency of TB in the population is 7%. (b) The frequency of TB in the population is 50%.
Most medical tests are not completely accurate. For example, a microscopy test for TB comes out positive with probability 0.01 when the tested individual doesn't actually have TB, and it comes out negative with probability 0.2 when the tested individual does have TB. Find the probability that a randomly chosen individual will test positive under the following conditions. (a) The frequency of TB in the population is 7%. (b) The frequency of TB in the population is 50%.Explanation / Answer
as probabilty of +ve result =P(having TB and +ve result +not having TB and +ve result)
a) for 7% ; probabilty of positive result =0.07*0.8+0.93*0.01=0.0653
b) for 50%, probabilty of positive result =0.5*0.8+0.5*0.01=0.405
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