Question

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 ___________

Answer 1

Answer: See explanation

Step-by-step explanation:

Expected payoff from first strategy = (Prob. of Success)*Payoff under success+(Prob. of failure)*Payoff under failure

1) The expected payoff from the first strategy (investing everything in Project X) will be:

= (90% × 30000 + 10% × -20000)

= 0.9 × 30000 + 0.1 × (-20000)

= $27000 - $2000

= $25000.

2) Probability that both will succeed will be:

= (Prob. Of X’s success) × (Prob. of Y’s success)

= 0.9 × 0.9

= 0.81

3) Probability that both will fail will be:

= (Prob. Of X’s failure) × (Prob. of Y’s failure)

= 10% × 10%

= 0.1 × 0.1

= 0.01

4) Probability that one project fail and one project will succeed will be:

= (Prob. Of X’s success) × (Prob. of Y’s failure) + (Prob. Of X’s failure) × (Prob. of Y’s success)

= (0.9 × 0.1) + (0.1 × 0.9)

= 0.09 + 0.09

= 0.18