Sum of two dice

What this probability counting question tests

This is a foundational probability question that appears regularly in quant interviews because it exposes a common mistake: confusing ordered and unordered outcomes when building a sample space. It tests whether you understand that probability depends on how you define your sample space, and that not all ways of counting outcomes are equally valid.

The problem asks you to find the probability of a specific sum and then explain why a seemingly natural approach—counting unordered pairs—leads to an incorrect result. This requires you to reason carefully about what "equally likely" means and why some sample spaces preserve that property while others do not. Firms value this kind of metacognitive clarity: knowing not just how to compute an answer, but why certain methods fail.

• Sample space construction and size
• Equally likely outcomes vs. compound events
• Ordered vs. unordered counting
• Symmetry and bias in outcome enumeration