Hatcheck Disaster

What this expectation and variance question tests

This is a medium-difficulty probability question commonly asked at quant trading firms to assess your ability to compute expected value and variance using linearity and indicator variables. It combines conceptual clarity with practical calculation—neither brute-force enumeration nor heavy computation is required if you set up the problem correctly.

The classic approach uses indicator random variables and exploits linearity of expectation to avoid working directly with the joint distribution. Finding the variance requires understanding covariance structure and recognizing which pairs of events are dependent. The question rewards clean problem decomposition and the ability to reason about dependencies without getting lost in algebra.

• Linearity of expectation
• Indicator random variables
• Variance decomposition and covariance
• Symmetry and exchangeability in permutations