1) A diagnostic test for a disease is said to be 90% accurate in that if a perso
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Question
1) A diagnostic test for a disease is said to be 90% accurate in that if a person has the disease, the test will detect it with probability 0.9. Also, if a person does not have the disease, the test will report that he or she does not have it with probability 0.9. Only 1% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that she has the disease, what is the conditional probability that she does, in fact, have the disease? Are you surprised by the answer? Hint: Use Bayes FormulaExplanation / Answer
person has the disease = 0.01
P(test will detect | person has the disease) = 0.9
P(test will not detect | person has not the disease) = 0.9
P(test will detect | person has not the disease) = 1 - P(test will not detect | person has not the disease) = 1 - 0.9 = 0.1
P(test will detect) = P(test will not detect | person has not the disease) * P(person has not the disease) + P(test will detect | person has not the disease) * P(person has not the disease)
= 0.9 * 0.01 + 0.1 * 0.99
= 0.108
P(person has the disease | test will detect) = P(test will not detect | person has not the disease) * P(person has not the disease) / P(test will not detect)
= 0.9 * 0.1 / 0.108
= 0.833
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