6. A diagnostic test has a probability 0.95 of giving a positive result when app

Question

6. A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability 0.10 of giving a (false) positive when applied to a non-sufferer. It is estimated that 0.1 % of the population are sufferers. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this population). Calculate the following probabilities: 20 pts (a) that the test result will be positive Answer b) that, given a positive result, the person is a sufferer Answer (e) that, given a negative result, the person is a non-sufferer Answer: (d) that the person will be misclassified Answer:

Explanation / Answer

a) probabiliy that test will be positive =P(person suffers and postive result+no suffers and postiive result)

=0.001*0.95+(1-0.001)*0.1=0.10085

b) person is sufferer given positive result =P(person suffers and postive result)/P(test positive)=0.001*0.95/0.10085

=0.00942

c) probability of negative result =1-P(test positve) =1-0.10085=0.89915

therefore probability of non sufferer given test negative=P(non sufferer and test negative)/P(test negative)

=0.999*0.9/0.89915=0.9999444

d) probability person will be misclassified =P(non sufferer and test positive+person is sufferer and test negative)

=0.999*0.1+0.001*0.05=0.09995

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