The Forgetful Bus Driver

What this probability interview question tests

This is a classic easy-to-medium difficulty probability puzzle that appears across quantitative interviews. It rewards clean reasoning over brute-force enumeration, testing whether you can spot an elegant structure beneath apparent complexity.

The setup involves a sequence of random choices and conditional outcomes—superficially it looks like you might need to track 100 different scenarios, but the key insight is recognizing a symmetry that simplifies the entire problem. Interviewers use this question to see if you can zoom out, identify what actually matters, and avoid unnecessary computation.

• Symmetry and invariants in probability
• Recursive or inductive reasoning
• Simplifying complex multi-stage problems