Suppose that a pharmaceutical company has developed a new screening test for pancreatic cancer. Suppose that the tests have the following results: 19 out of 20 people known to have pancreatic cancer receive a positive result from the screening test, while 49 out of 50 people known not to have pancreatic cancer receive a negative result from the test. Finally, suppose that this screening test is designed to be given only to a target population that exhibits a set of symptoms that are possible indicators of pancreatic cancer -- experience shows that 1 out of 10 people in this population will actually have pancreatic cancer.

1. Draw a tree diagram representing the different possible outcomes and then input the specified conditional probabilities below. (6 pts.)

Pr(P|C) = Pr(P|~C) =

Pr(N|C) = Pr(N|~C) =

2. How reliable is this test for pancreatic cancer with respect to the target population? Consider the following set of questions: a) What is the probability that a person tested has cancer given that the test result is positive?, b) What is the probability that a person tested does not have cancer given that the test result is positive?, c) What is the probability that a person tested has cancer given that the test result is negative?, and d) What is the probability that a person tested does not have cancer given that the test result is negative? Use Bayes' rule to solve them. (4 pts.)

a) Pr(C|P) = b) Pr(~C|P) =

c) Pr(C|N) = d) Pr(~C|N) =

Please put answers and explanation seperately.