Suppose the probability that Professor Liebner gives you a problem that he thinks is easy is 0.8. Suppose that you think the problem is easy is 0.4. Suppose the probability that neither you nor Prof. Liebner think the problem is easy is 0.15.

a) What is the probability that at least one of you or Prof. Liebner think the problem is easy?

b) What is the probability that exactly one of you or Prof. Liebner think the problem is easy?

c) If you did not think the problem was easy, what is the probability that Prof. Liebner also did not think it was easy?

d) If Prof. Liebner did not think the problem was easy, what is the probability that you thought it was easy?

e) Are the events "Prof. Liebner thinks the problem is easy" and "you think the problem is easy" independent? Explain.