Will two croissants cover five customers?

What this inventory-probability interview question tests

This is a medium-difficulty probability question commonly used by quantitative trading and finance firms to assess how candidates handle discrete probability distributions under real-world constraints. The setup—a limited resource, independent customer choices, and a pass/fail outcome—mirrors problems in risk management and operational planning.

To solve it, you need to identify which customer sequences result in stockout (running out of croissants before all five are served) and either enumerate them or use a distributional argument. The key insight is recognizing that the stock is sufficient only if the number of croissant requests stays within bounds. Interviewers value clear problem setup, correct probability logic, and accurate computation over speed.

• Binomial distributions and threshold events
• Cumulative probability and complementary counting
• Independence and joint probability