Business, 24.05.2021 14:00 averylivinglife2041

Sam is considering two investment strategies. The first strategy involves putting all of his available funds in Project X. If Project X succeeds, he will receive a $30,000 return, and if it fails, he will suffer a $20,000 loss. There is a 90% chance Project X will succeed and a 10% chance it will fail. The second strategy involves diversification: investing half of his funds in Project X and half of his funds in Project Y (which has the same payoff structure as Project X).

If both projects succeed, he will receive a $15,000 return from Project X and a $15,000 return from Project Y, for a net gain of $30,000.
If both projects fail, he will suffer a $10,000 loss on Project X and a $10,000 loss on Project Y, for a net loss of $20,000.
If one project succeeds and one fails, he will receive a $15,000 return from the successful project and will suffer a $10,000 loss on the failed project, for a net gain of $5,000.

As with Project X, there is a 90% chance that Project Y will succeed and a 10% chance that it will fail. Assume that the outcomes of Project X and Project Y are independent. That is, the success or failure of Project X has nothing to do with the success or failure of Project Y.

The expected payoff from the first strategy (investing everything in Project X) is :

Suppose Sam chooses the second strategy, which is putting half of his funds in Project X and half into Project Y. The probability that both projects will succeed is , the probability that both projects will fail is and the probability that one project will fail and one project will succeed is

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