I am having issues with understanding a question on an assignment:
A test for the presence of a certain disease has probability 0.05 of giving a false-positive reading and probability 0.04 of giving a false-negative result. Suppose that four individuals are tested, three of whom do not have the disease and one of whom does. Let X= the number of positive readings.
- Does X have a binomial distribution?
- Find the probability that only one of the four test results is positive.
Edit: I'm not sure if this is correct, but I have the probability setup like this: P(A->P)P(B->N)P(C->N)P(D->N)+P(A->N)P(B->P)P(C->N)P(D->N)+P(A->N)P(B->N)P(C->P)P(D->N)+P(A->N)P(B->N)P(C->N)P(D->P)
Where A,B and C do not have the disease. D has the disease. (A->P means A tests positive)