Fair Price for the Series

What this expected-value interview question tests

This is an easy probability question that introduces the famous St. Petersburg Paradox—a foundational puzzle in decision theory and expected value reasoning. Quant firms use it to see whether candidates can set up a simple infinite series, compute expected value correctly, and then think critically about why mathematical expectation sometimes diverges from real-world behaviour.

The question rewards two things: first, the ability to identify and sum a geometric series under a repeated-trial setup; second, the insight that expected value alone does not explain human choice. You'll need to think about utility, risk aversion, and the difference between theoretical infinity and practical decision-making.

• Infinite expected value and convergence of probability series
• Utility theory and why humans exhibit bounded willingness-to-pay
• The gap between mathematical expectation and rational economic behaviour