**Instructions**: Answer each question, and when required explain your answer. Your explanation must be clear and complete. You may refer to your book, your notes and your homework papers. You may use a calculator.
- An experiment is run consisting of randomly picking a consonant and a vowel
from the sentence "Math is fun!"
- How many elements are in the sample space?
- Find the probability that the letters picked include "t" or "h" but not "u". Explain how you obtained your answer.

- Consider Problem 6, p. 687.
- (a) Do 6(a).
- (b) Do 6(b). How are these three probabilities related?
- (c) Find P(M∩C), P(N∩C) and P(C). How are these three probabilities related?
- (d) Find and interpret P(C | N).
- (e) Find and interpret P(N | C).

- Suppose a screening test for a certain virus is positive 99% of the time for infected people and 3% of the time for uninfected people. Also suppose that 0.5% of the population is infected.
- (a) Draw a probability tree diagram for the experiment that consists of
randomly picking a person, who may be either infected or healthy, and then giving the person the test.
- (b) What is the chance that the person is infected?
- (c) What is the chance that the person tests positive given that
the person is not infected?
- (d) What is the chance that the person is not infected given that the test is positive?

- Problem 34a, p. 691.