3.72 An analyst attempting to predict a corporation’s earnings next year believes that the corporation’s business is quite sensitive to the level of interest rates. He believes that, if average rates in the next year are more than 1% higher than this year, the probability of significant earnings growth is 0.1. If average rates next year are more than 1% lower than this year, the probability of significant earnings growth is estimated to be 0.8. Finally, if average interest rates next year are within 1% of this year’s rates, the probability for significant earnings growth is put at 0.5. The analyst estimates that the probability is 0.25 that rates next year will be more than 1% higher than this year and 0.15 that they will be more than 1% lower than this year.

a. What is the estimated probability that both interest rates will be 1% higher and significant earnings growth will result?

b. What is the probability that this corporation will experience significant earnings growth?

c. If the corporation exhibits significant earnings growth, what is the probability that interest rates will have been more than 1% lower than in the current year?