Assume an investor wants to build a hotel in an area where hurricanes occasionally hit.Suppose that hurricanes could be strong, medium or weak. The investor has to decide how much  to reinforce the buildings at the hotel complex. Hotel can be reinforced to withstand a strong,  medium or weak hurricane. Probabilities of having a strong, medium, and weak hurricane in the  area are 5%, 20%, and 75% respectively.

• If hotel is built to withstand a strong hurricane, it will cost 40 million dollars and it will  not be damaged in any kind of hurricane.
• If hotel is built to withstand a medium hurricane, it will cost 30 million dollars and it will  not be damaged in a medium and weak hurricane, but it will take 25 million dollars  damage in a strong hurricane.
• If hotel is built to withstand a weak hurricane, it will cost 25 million dollars, it will take  20 and 35 million dollars damage in a medium and strong hurricane, respectively, but it  will not be damaged in a weak hurricane.
The investor can buy a hurricane forecast service from National Hurricane Center (NHC) that  predicts hurricane strength.
• If the hurricane is strong: 
o NHC predicts a strong hurricane correctly in 75% of the time 
o NHC predicts a medium hurricane incorrectly in 20% of the time 
o NHC predicts a weak hurricane incorrectly in 5% of the time 
• If the hurricane is medium: 
o NHC predicts a strong hurricane incorrectly in 10% of the time 
o NHC predicts a medium hurricane correctly in 70% of the time 
o NHC predicts a weak hurricane incorrectly in 20% of the time 
• If the hurricane is weak: 
o NHC predicts a strong hurricane incorrectly in 10% of the time 
o NHC predicts a medium hurricane incorrectly in 10% of the time 
o NHC predicts a weak hurricane correctly in 80% of the time 

a) Calculate all the required probabilities (3 marginal and 9 conditional). 
b) Calculate the EMV without information. 
c) Calculate the EMV with perfect information. 
d) Calculate the EMV with imperfect information.
e) Calculate the EVI. 
f) Calculate the EVII.