Question

A certain medical disease occurs in 5% of the population. A simple screening procedure is available and in 3 out of 10 cases where the patient has the disease it provides 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. Draw a tree diagram to represent this.
a) Find the probability that a randomly selected individual
does not have the disease but gives a positive result in the screening test
gives a positive result on the test.
b) Ben has taken the test and his result is positive. Find the probability that he has the disease