Birthday match among three

What this birthday-collision probability question tests

This is a classic medium-difficulty probability question that appears frequently in quant interviews. It tests whether you can set up and solve a problem involving at least one constraint—a phrasing that often trips up candidates who haven't internalized the complement rule.

The core skill is recognizing when it's easier to compute the complement (no matches) rather than enumerate all matching cases. You'll need to think carefully about conditional probabilities as you remove people from the room one at a time, and then convert your result into the form the question asks for. The calculation itself is straightforward once the setup is right.

• Complement rule and negation
• Conditional probability and sequential reasoning
• Uniform distributions over discrete outcome spaces