Question

In a laboratory, blood test is 95% effective in detecting a certain disease, when it is, in fact, present. However, the test also yields a false positive (test is positive but patient does not have the disease) result for 1% of the healthy people tested. 0.5% of the population actually has the disease. Given this information, calculate the following probabilities:

1. The probability that the test is positive.
2. Given a negative result, the probability that the person does not have the disease.
3. The probability that the person will be misclassified (either false positive or false negative -test is negative but patient has the disease-)

Answer 1

a)

P(tested positive) =P(have disease)*P(tested positive |have disease)+P(not have disease)*P(tested positive |not have disease)

=0.005*0.95+(1-0.005)*0.01

=0.0147

b)

P(not have |tested negative)

=P(not have disease)*P(tested negative |not have disease)/P(tested negative)

=(1-0.005)*(1-0.01)/(1-0.0147)=0.9997

c)

P(missclassifed) =P(have disease)*P(tested negative |have disease)+P(not have disease)*P(tested positive |not have disease)

=0.005*(1-0.95)+(1-0.005)*0.01=0.0102