A medical report shows that the carriers of a particular dis

A medical report shows that the carriers of a particular disease during winter months constitute 2% of the population.

(a) Let X be the number of carriers in a random sample of 15 taken from this population. What is the distribution of X? Find the probability that exactly 2 of the people in the sample are carriers of this disease.

(b) test is 90% accurate in detecting both presence and absence of the diease in a person. Show that the probability of a false positive result (ie that a non-carrier is incorrectly identified as being a carrier) is 0.098. Given a person gets a positive result, what is the probability that the person is a non-carrier?

Solution

Best way to view this is to view it as TWO dependent events.

a) simply use r studio and use dbinom(2, 15, 0.02)

b) Use a tree diagram

P(S) = 0.9 P(NS) = 0.1

P(disease) = 0.02 P(nodisease) = 0.98

therfore to get a false positive (0.1 X 0.98) and for the second section of b is just (0.01 X 0.02)