Entry fee for a game paying one die face

Question

I will roll one fair die and pay you as many dollars as the number on top. What is the most you should pay to play if the game is to be fair?

Short answer

$3.50. A fair entry fee is the expected payout, and the average of the faces $1$ through $6$ is $3.5$ .

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q3.1, p.80; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Expectation, Mean, and Variance
Counting and Combinatorics
Conditional Expectation and Variance Revisited

Start with a free lesson: Expectation, Variance and Covariance is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free