Fair Die Ticket Price

This question presents a simple gambling setup based on rolling a fair die and receiving a payout tied directly to the outcome. The candidate is asked to determine the fair entry price to play the game, in the sense that neither the player nor the organizer has an inherent long-term advantage. It is an archetypal expected-value problem, often used in the early stages of quantitative interviews, probability screens, and internship or graduate-level assessments to check that the basics of discrete random variables are firmly understood.

The discussion leans on calculating the expected value of a discrete uniform distribution and interpreting that value as a break-even price. An interviewer is watching for a clean definition of expected value, correct use of outcome–probability pairs, and the ability to justify fairness in terms of long-run averages rather than intuition. They may also look for concise algebra, comfort with simple summations, and a clear verbal explanation connecting the numerical result back to the economic idea of a fair game.

What it tests

Whenever a game of chance pays out according to the value of a random variable, the fair price is determined by the expected value of that variable. The expected value is a weighted average, where each possible outcome is multiplied by its probability and summed. This principle holds because, over many repetitions, the average payout converges to the expected value, ensuring neither player nor house has a systematic advantage. The fairness is rooted in the Law of Large Numbers: in the long run, the mean outcome per play approaches the expected value, so setting the ticket price to this value balances the game. This approach applies to any random process with known discrete outcomes and probabilities, not just dice.