Consider two possible prizes:

Prize A offers a 10% chance to win $300.

Prize B offers $25 for sure.

Given the choice between these two prizes, Roy prefers Prize B over Prize A. (He also, unsurprisingly, prefers Prize A over no prize at all.)

Now consider several other possible prizes:

Prize Y: a 5% chance to win $300

Prize Z: a 50% chance to win $25

Given his preference above, determine a possible preference ordering for Roy across all four options (A, B, Y, Z), assuming his preferences are consistent with expected utility theory. Show your work and/or explain your reasoning.

Roy's favorite prize is:

Roy's 2nd favorite prize is:

Roy's 3rd favorite prize is:

Roy's 4th favorite prize is: