Your company needs to make an important decision that involves large monetary consequences. You have listed all of the possible outcomes and the monetary payoffs and costs from all outcomes and all potential decisions. You want to use the EMV criterion, but you realize that this requires probabilities and you see no way to find the required probabilities. What can you do$?$

If your company makes a particular decision in the face of uncertainty, you estimate that it will either gain $$10,000,$ gain $$1,000,$ or lose $$5,000,$ with probabilities $0\mathrm{.}40,0\mathrm{.}30,$ and $0\mathrm{.}30,$ respectively. You $($correctly$)$ calculate the EMV as $$2,800.$ However, you distrust the use of this EMV for decision$-$making purposes. After all, you reason that you will never receive $$2,800$; you will receive $$10,000,$ $$1,000,$ or lose $$5,000.$ Discuss this reasoning.

In the previous question, suppose you have the option of receiving a check for $$2,700$ instead of making the risky decision described. Would you make the risky decision, where you could lose $$5,000,$ or would you take the sure $$2,700?$ What would influence your decision?

Your company has signed a contract with a good customer to ship the customer an order no later than $20$ days from now. The contract indicates that the customer will accept the order even if it is late, but instead of paying the full price of $$10,000,$ it will be allowed to pay $10\%$ less, $$9,000,$ due to lateness. You estimate that it will take anywhere from $17$ to $22$ days to ship the order, and each of these is equally likely. You believe you are in good shape, reasoning that the expected days to ship is the average of $17$ through $22,$ or $19\mathrm{.}5$ days. Because this is less than $20,$ you will get your full $$10,000.$ What is wrong with your reasoning?

It seems obvious that if you can purchase information before making an ultimate decision, this information should generally be worth something, but explain exactly why $($and when$)$ it is sometimes worth nothing.