The Management of Ore must choose whether to go ahead with either of two mutually exclusive projects, A and B$.$ The payoff of projects depend on the eventual demand condition which will be strong with probability $30\%$ and weak with $70\%.$ If the company invests in Project A they will earn $$4000$ if there is strong demand and will lose $$1000$ if there is weak demand. If the company invests in Project B they will earn $$1500$ if there is strong demand and will earn $$500$ if there is weak demand.

a$)$ Calculate the value of perfect information of an expert which tells the company eventual demand condition with $100\%$ accuracy prior to the decision on investment.

Now assume that, in the past, the expert has predicted strong demand $25\%$ of the time and were correct $72\%$ in those cases. In those cases the expert predicted weak demand they were correct $84\%$ of the time. Calculate the expected value of imperfect information.