Your inheritance, which is in a blind trust, is invested entirely in McDonald's or in U.S. Steel. Because the trustee owns several McDonald's franchises, you believe the probability that the investment in McDonald's is 0.8. In any one year, the return from an investment in McDonald's is approximately normally distributed with mean 14% and standard deviation 4%, while the investment in U.S. Steel is approximately normally distributed with mean 12% and standard deviation 3%. Assume that the two returns are independent.

a. What is the probability that the investment earns between 6% and 18% (i) if the trust is invested entirely in McDonald's, and (ii) if the trust is invested entirely in U.S. Steel?

b. Without knowing how the trust is invested, what is the probability that the investment earns between 6% and 18%?

c. Suppose you learn that the investment earned more than 12%. Given this new information, find your posterior probability that the investment is in McDonald's.