The Last Ace

What this expected-position interview question tests

This is a medium-difficulty probability question that appears in quant interview rounds to assess whether a candidate can reason about order statistics and symmetry in a uniform random shuffle. It rewards insight over brute-force enumeration.

The core skill being tested is the ability to set up and solve for an expected value when outcomes are constrained by a finite structure (in this case, the positions of special items in a permutation). Candidates who approach this cleanly typically exploit symmetry or combinatorial counting rather than building up probabilities case-by-case. Interviewers are looking for structured reasoning and the ability to translate a real-world shuffling scenario into precise mathematical language.

• Order statistics in uniform random permutations
• Symmetry and exchangeability
• Linearity of expectation applied to position problems