First Ace

What this expected-value interview question tests

This is a medium-difficulty probability question that asks you to find the expected value of a stopping time—in this case, the draw number at which you first encounter a target card. It's the kind of problem quant trading desks use to assess whether you can set up and solve expectation problems cleanly, without relying on heavy computation.

Solving it requires you to think carefully about the structure of the problem: how many cards remain in the deck, what the probability of drawing an Ace is at each step, and how to aggregate these probabilities into a single expectation. The key insight is often to avoid brute-force enumeration and instead use a more elegant counting or symmetry argument.

• Expectation of a discrete random variable
• Geometric-type waiting times and stopping rules
• Symmetry and exchangeability arguments
• Conditional expectation and recursion