Heads on the Last Flip

What this conditional-probability interview question tests

This is an easy probability question that appears in quant interviews at firms like Bridgewater. It tests whether you can reason clearly about conditional probability and avoid a common intuitive trap.

The setup involves a geometric process—flipping a fair coin until the first heads—and asks you to reason about the final flip given that the process has already terminated. The key insight is recognizing what information the conditioning statement actually provides, and whether it changes the probability of the outcome you are being asked about. Candidates who confuse the sample space or misread the conditioning often arrive at an incorrect answer.

• Geometric distributions and stopping times
• Conditional probability and Bayes' rule
• The relationship between the event that defines the stopping rule and the event being queried