Conditional Probability with Two Dice

What this conditional probability interview question tests

This is an easy probability question that appears frequently in quant interviews because it requires clean reasoning about conditional probability rather than heavy computation. It tests whether you can correctly identify a restricted sample space and count favorable outcomes within it.

To approach problems like this, start by defining the event you are conditioning on (the constraint), enumerate all outcomes that satisfy it, then count how many of those also satisfy the target event. The key is avoiding the trap of working in the original sample space instead of the conditional one. Interviewers use these questions to see if your probabilistic reasoning is sound and whether you can simplify fractions and express answers clearly.

• Sample space restriction under a condition
• Counting favorable outcomes in a constrained space
• Bayes' theorem as an alternative framework