Money in the Bank

What this expected-value interview question tests

This is an easy probability question that asks you to compute the expected value of a bankroll after a series of random outcomes. It is the kind of warm-up question quant trading desks use to check whether a candidate can quickly set up and reason about expected value under a simple, repeated random process.

To solve problems like this, identify the distribution of a single outcome (in this case, the gain or loss from one die roll), compute its expectation, then apply linearity of expectation across all independent rolls. The key insight is that you do not need to enumerate all possible final states—you can work with expectations directly and let them add up.

• Expectation of a discrete random variable
• Linearity of expectation across independent trials
• Distinguishing between the expected value and the distribution of outcomes