Are we in St. Petersburg?

What this St. Petersburg paradox question tests

This is an easy probability question that introduces the famous St. Petersburg paradox—a foundational puzzle in decision theory and expected value. It asks you to compute the expected value of a simple payoff structure tied to a geometric random variable (the first occurrence of heads in fair coin flips).

The question rewards careful setup of an infinite sum and recognition of a classic result in probability. Most candidates can write down the expected value formula and begin evaluating it; the key is handling the infinite series correctly and understanding why the answer surprises intuition. Interviewers use this to probe whether you can reason rigorously about infinite expectations and recognize when a naive expected-value calculation yields a counterintuitive outcome.

• Geometric distributions and first-passage times
• Infinite series and convergence
• Expected value under unbounded payoffs
• Rational decision-making under risk