Two Random Draws Expected Payout

This quant interview question is about computing an expected payout when sampling randomly from a finite set with replacement. It fits squarely into the core expected value toolkit often seen in quant prep, blending a clean payoff rule with a uniform discrete distribution. Because the setup is simple and fully specified, it isolates pure expectation reasoning without distractions from market microstructure or stochastic calculus.

It trains your understanding of expected value for discrete random variables and your ability to extend that to multiple random draws. It reinforces thinking in terms of random variables and payoff functions, how scaling a payoff affects its expectation, and how repeated, identical experiments contribute to a total reward.

This matters for quant interviews because so many trading, risk, and pricing problems reduce to computing expectations quickly and reliably. Interviewers want to see you translate a story into a random variable framework, manage repeated draws fluently, and reason about payoff structures under uncertainty. Strong performance here signals readiness for more complex quant questions that layer in dependence, conditioning, or continuous distributions, which are central in trading strategy design and risk modeling across modern quantitative finance interviews.

What it tests

The key structure in this class of problems is the linearity of expectation, which states that the expected value of a sum of random variables is the sum of their expected values, regardless of whether the variables are independent. This principle allows you to decompose a complex expected value calculation into simpler parts, often reducing the problem to finding the expected value of a single component and scaling it appropriately. In problems involving identical, independent random draws, each draw contributes equally to the total expectation, so you can compute the expected value for one and multiply by the number of draws. The payout function being linear (here, a constant multiple of the sum) means the scaling factor can be factored out before taking expectations. This structure holds because expectation is a linear operator, and so additive and multiplicative constants can be handled outside the expectation, simplifying calculations significantly.