probability

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 

Answer 1

p(disease)= p(d) = 5% = .05 p(~d)=95%=.95

p(d/+) = p(disease if test positive) = 50% = .5

P(d/-) = p(disease if test negative) = .05 = 5%

find p(~d/+)

use Bayes theorem

p(~d/+)= p(d/-)p(-)/p(+)= .05(.95)/.05=.95= 95%

b) ben has 5% chance

the test is useless