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.

• [1] (10 points) Problem 12 on p. 646. Also, for each of the parts (a) through (e) of this Problem, determine the theoretical probability of the event given in each part, assuming that the die and the coin are fair (i.e, that each side is equally likely to come up).
• [2] (10 points) Problem 17 on p. 666.
• [3] (5 points) Problem 5 on p. 687.
• [4] (5 points) Suppose a screening test for a certain virus is positive 95% of the time for infected people and 2% of the time for uninfected people. Also suppose that 1% 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?