Answer to Question #127101 in Discrete Mathematics for tharushika

Question

3. A certain medical disease occurs in 1% of the population. A simple screening procedure is available and in 8 out of 10 cases where the patient has the disease, it produces a positive result. If the patient does not have the disease there is still a 0.05 chance that the test will give a positive result. Find the probability that a randomly selected individual:

(a) Does not have the disease but gives a positive result in the screening test
(b) Gives a positive result on the test
(c) Nilu has taken the test and her result is positive. Find the probability that she has the disease.

Answer 1

a) P(C' $\bigcap$ S)=0.99*0.05=0.0495

b) P(S)=P(C â‹‚ S)+P(C' â‹‚ S)=0.01*0.8+ 0.99*0.05=0.0575

c)P(C|S)=P(C â‹‚ S)/P(S)=0.01*0.8/0.0575=0.139