An analyst attempts to predict a corporation's earnings next year. She believes that, if the average interest rate in the next year is greater than 2.5%, the probability of signicant earnings growth is 0.1. If the average rate next year is lower than 2%, the probability of signicant earnings growth is estimated to be 0.8. Finally, if the average interest rate next year is between 2% and 2.5%, the probability of signicant earnings growth is put at 0.5. The analyst estimates that the probability is 0.25 that the rate next year will be greater than 2.5% and 0.15 that it will be lower than 2%.

(a) What is the estimated probability that the average interest rate next year is NOT lower than 2%?

(b) What is the estimated probability that the average interest rate will be greater than 2.5% and signicant earnings growth will realize next year?

(c) What is the estimated probability that the average interest rate will be NO lower than 2% and signicant earnings growth will realize next year?

(d) What is the probability that this corporation will experience signicant earnings growth next year?

(e) Suppose that the corporation exhibits signicant earnings growth next year. Given this observation, what is the conditional probability that the average interest rate have been greater than 2.5%? (f) What is the conditional probability that this corporation will experience signicant earnings growth given that the average interest rate next year is NO lower than 2%?