1. You are tracking correlation of two funds, Fund A and Fund B. Examining current quarter data to date, the probability of Fund B exceeding its performance benchmark is 0.75 and the probability of Fund A exceeding its performance benchmark is 0.60. However you note that if Fund B exceeds its benchmark, the likelihood of Fund A exceeding its benchmark increases to 0.65. Given this condition, what is the probability that both funds will exceed their respective benchmarks?
a. 0.4500
b. 0.4875
c. 0.5000
d. 0.6500
2. ARI Market Forecasting incorporates a sophisticated macroeconomic model incorporating 42 variables to forecast where the market will end up (up or down) at the end of the calendar year. Actually, ARI bases their forecast on whether the NFC will win the Super bowl (market rises) or the AFC will win the Super bowl (market declines). If the NFC wins, ARI gives a 0.60 probability that the market will rise and a 0.45 probability that the market will rise if the AFC wins. The bookies give 2:1 odds that the NFC will win the Super bowl. What is the probability that the market will rise for the upcoming year?
a. 0.27
b. 0.48
c. 0.55
d. 0.67
3. An analyst expects that 10% of all publicly traded companies will experience a decline in earring per share (EPS). She developed a ratio to help forecast a decline in a company's EPS: if a company is headed for an EPS decline, there is a 70% probability that the ratio will be negative. If the company if not head for an EPS decline, there is a 20% probability that the ration will be negative. The analyst randomly selected a company and its ratio is negative. Based on Bayes' theorem, the posterior probability that the company will experience an EPS decline next year IS closest to:
a. 7%
b. 10%
c. 18%
d. 28%