The expected value of perfect information is:
A)4 5
B)9
C)40 5
D)49 5
E)60

Question

The expected value of perfect information is:
A)4 5 
B)9 
C)40 5 
D)49 5 
E)60

Quizplus · Accepted Answer

The expected value of perfect information is equal to the difference between the expected value of the best decision with perfect information and the expected value of the best decision without perfect information.

In this case, without perfect information, the best decision is to choose the option with the highest expected value. A quick calculation shows that Option 2 has the highest expected value of 9 (0.4 x 6 + 0.6 x 3).

Now let's assume we have perfect information and know which coin flip will come up. If the coin comes up heads, then Option 1 has an expected value of 10 (0.4 x 5 + 0.6 x 3), and if the coin comes up tails, then Option 3 has an expected value of 9 (0.4 x 4 + 0.6 x 10).

Taking the average of these two values (0.5 x 10 + 0.5 x 9 = 9.5), we see that with perfect information, the expected value of the best decision is 9.5.

Therefore, the expected value of perfect information is 9.5 - 9, or 0.5. Since this value is positive but relatively small, we can conclude that Option 2 with an expected value of 9 is the best choice.

The Expected Value of Perfect Information Is