Larry 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 $10,000 return, and if it fails, he will suffer a $2,000 loss. There is a 70% chance Project X will succeed and a 30% 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 $5,000 return from Project X and a $5,000 return from Project Y, for a net gain of $10,000.
If both projects fail, he will suffer a $1,000 loss on Project X and a $1,000 loss on Project Y, for a net loss of $2,000.
If one project succeeds and one fails, he will receive a $5,000 return from the successful project and will suffer a $1,000 loss on the failed project, for a net gain of $4,000.
As with Project X, there is a 70% chance that Project Y will succeed and a 30% 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 :
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