Three dice, one number

Expected value of a dice-rolling betting game

This is an easy probability question that tests your ability to set up and compute expected value in a discrete outcome space. It's the kind of foundational reasoning that quant firms expect candidates to execute cleanly and quickly, without error.

To solve it, you'll identify all possible outcomes (no dice match, exactly one matches, exactly two match, all three match), assign a probability to each using combinatorics, then weight the payout or loss by its probability. The key is organizing the calculation so that your arithmetic stays accurate and your final answer is expressed as a simplified fraction. Once you have the expected value, interpreting whether the bet is favourable requires only a comparison to zero.

• Binomial probability (outcomes from repeated independent trials)
• Payout structure and net profit/loss per outcome
• Linearity of expectation across mutually exclusive cases