11. suppose that a medical test has a 92% chance of detecting adisease if the pe
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Question
11. suppose that a medical test has a 92% chance of detecting adisease if the person has it (i.e., 92% sensitivity) & a 94%chance of correctly indicating that the disease is absent if theperson really does not have the disease (i.e., 94 % specificity).suppose 10% of the population has the disease. a.) what is the probability that a randomly chosen person willtest positive?b.) suppose that a randomly chosen person does test positive.what is the probability that this person really has thedisease? a.) what is the probability that a randomly chosen person willtest positive?
b.) suppose that a randomly chosen person does test positive.what is the probability that this person really has thedisease?
Explanation / Answer
a) p(disease + ) *p(Test + | Disease +) = 0.10 * 0.92 =0.092 b) Sensitivity = True Positive / (True Positive + False Positive) This means that the test is correct in 94% of the cases. Therefore,the probability to have the disease if someone is sick is 0.94
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