Suppose it is known that 1 of the population suffers from a

Suppose it is known that 1% of the population suffers from a particular disease. A blood test has a 97% chance of identifying the disease for diseased individuals, but also has a 6% chance of falsely indicating that a healthy person has the disease.

a) What is the probability that a person will have a positive blood test?

b) If your blood test is positive, what is the chance that you have the disease?

c) If your blood test is negative, what is the chance that you do not have the disease?

Solution

Thus,
P(C)=.01, P(B|C)= .97 , and P(P|C\') =.06
Let C denote the event that a randomly selected person is a carrier of the disease.
Let P denote the event that the blood test is positive.

a) what is the probability that a person will have a positive blood test P(P).
P(P)= (0.1)(0.97)+(0.99)(0.06)= 0.0691

b) If your blood test is positive, what is the chance that you are a carrier of the disease?
(C|P) = 0.0097/0.0691= 0.14

c) If your blood test is negative, what is the chance that you are not a carrier of the disease?
(C\'|P\')= 0.9306/ 0.9309 = 0.9997