1: Compute the probability that a person who tests positive actually has the disease. (You may find it useful to construct a probability contingency table.)

Question

1: A certain disease has an incidence rate of 0.5%. The false negative rate on a test for the disease is 5%; the false positive rate is 5%. Compute the probability that a person who tests positive actually has the disease. (You may find it useful to construct a probability contingency table.)

The probability a person who tests positive actually has the disease is   _________

Give your answer accurate to at least 3 decimal places.

Answer 1

positive Negative

disease 49.75 0.25 50

Nodiseasee 497.5 9452.5 9950

total 547.25

Take the total to be 10,000

0.5/100*10,000=50

10,000-50=9950

0.5/100*50=0.25-disease negative

49.75-no disease positive

5/100*9950=497.5-no disease positive

9452.5-no disease negative

P(disease/ positive)=49.75/547.25=0.091