1. 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.
2. 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).
3. 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?
4. Problem 34a, p. 691.