Problem 1: After its recent failures in the financial sector, Citigroup decided to change course and look for new investment opportunities. It can invest in exactly one of the following:

P1: Oil drilling in the North Sea. An investment of 4M$ is required. The possible outcomes are:A1 = Success 10%. Expected revenue 20M$.A2 = Failure. Expected revenue 1M$.

P2: Diamond mining in South America. An investment of 5M$ is required. The possible outcomesare:B1 = Success 30%. Expected revenue 15M$.B2 = Failure. Expected revenue 3M$.

P3: Producing a new Angelina Jolie movie. An investment of 5M$ is required. The possibleoutcomes are:C1 = Success 60%. Expected revenue 11M$.C2 = Failure. Expected revenue 2M$.

In addition, there is a 10% chance of a revolution in South America. In that case, any investmentthere is lost (even if diamonds are found).Answer the following questions and give thorough explanations of how to reach yourconclusions.

1. Calculate the EMV.

2. How much would the company be willing to pay for perfect information on the outcomes of P1 only?Diana Diamond can predict success in diamond mining. Her recommendations are YES (success)or NO (failure). It is known that:P(YES|B1) = 0.9 and P(NO|B2) = 0.8

3. How much would the company be willing to pay Diana for her recommendation?

4. The company hired Diana. She recommended YES. How much would thecompany be willing to pay for perfect information on the outcomes of P1 only?