The following is not so much a mathematical problem as a psychological problem, but it has to do with the subjective evaluation of outcomes.

PROBLEM 1: You start out with $60 in your wallet. You spend $20 on an advance general-admission ticket to a concert. You arrive at the concert hall, open your wallet, and find that the ticket is missing and presumably lost forever, but you still have $40. What would you do? Would you spend another $20 to buy another ticket? Or would you skip the concert? (There is no right or wrong answer here, but please consider your answer before you read the next paragraph.)

PROBLEM 2: You start out with $60 in your wallet. You head for the concert hall, planning to buy a ticket at the door. When you arrive, you open your wallet and find that $20 is missing and presumably lost forever, but you have $40 left. Now what would you do?

Someone did an actual survey. I don't remember the numerical results, but a large number of people - let's say half - when problem 1 was posed, said that they would skip the concert. When problem 2 was posed instead, nearly everyone said they would buy a ticket.

I will leave it to you to figure out what this says about human nature.