5x ROI

What this expected-value card game question tests

This is a straightforward expected-value problem common in probability interviews at trading firms. It asks you to compute the mean payout of a simple draw without replacement scenario, rewarding clear setup and correct application of linearity of expectation.

The core skill tested is your ability to identify what random variables matter, compute their individual expectations, and combine them correctly. Many candidates either overcomplicate the problem by worrying about dependence between draws, or make arithmetic errors when summing expectations. The "closest answer" format also means you should be able to estimate and sanity-check your result quickly.

• Linearity of expectation (applies even for dependent random variables)
• Symmetry and exchangeability in sampling without replacement
• Distinguishing between the expectation of a sum and the sum of expectations