# A diagnostic test for disease X correctly identifies the disease 93% of the time . False positives occur 9%. It is estimated that 2.09% of the population suffers from disease X. Suppose the test is applied to a random individual from the poplulation . compute the following probabilities .( It may help to draw a probability tree)*The percentage chance that , given a negative result , the person does not have disease X =      %*The percentage chance that , the person will be misclassified =    %

Question

A diagnostic test for disease X correctly identifies the disease 93% of the time . False positives occur 9%. It is estimated that 2.09% of the population suffers from disease X.

Suppose the test is applied to a random individual from the poplulation . compute the following probabilities .( It may help to draw a probability tree)

*The percentage chance that , given a negative result , the person does not have disease X =      %

*The percentage chance that , the person will be misclassified =    %

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Step 1

Given that

Probability of disease P(D) = 0.0209

Probability that a  diagnosis test identifies disease correctly P(Positive|Disease) = 0.93

Probability that tests positive if there is no disease( false positive) P(Positive | No disease) = 0.09.

we need percentage chance that given negative result person does not have disease.

P(No Disease | Negative) = P(No disease)*P(Negative|No disease)/P(Negative)

P(Negative|No disease) = 1 - P(positive|No disease) = 1 - 0.09 = 0.91

P(Negative|disease) = 1 - P(positi...

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