The test to detect the presence of a liver disorder is 98% accurate for a person who has the disease and 97% accurate for a person who does not have the disease. If 3.5% of the people in a given population actually have the disorder, what is the probability that a randomly chosen person tests positive?
The answer is 0.06325. The probability of detecting the true presence is 98% = 0.98. The probability of not detecting the true presence is: 100%-98% = 2% = 0.02. The probability of detecting the true absence is 97% = 0.97. The probability of not detecting the true absence is: 100%-97% = 3% = 0.03. The probability of having the disorder is: 3.5% = 0.035. The probability of not having the disorder is 100% - 3.5% = 96.5% = 0.965. The probabilty of having a disorder and detecting the true presence is: 0.035 * 0.98 = 0.0343. The probability of not having the disorder and detecting the true absence is: 0.965 * 0.03 = 0.02895. The probability that a randomly chosen person tests positive is: the probabilty of having a disorder and detecting the true presence + the probability of not having the disorder and detecting the true absence = 0.0343 + 0.02895 = 0.06325.
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