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What this conditional probability interview question tests

This is an easy probability question that uses observed evidence to update belief about an earlier event. It is a classic application of Bayes' theorem, the foundation of how traders and quants reason about updating probabilities in light of new information.

To solve problems like this, you set up the two scenarios (die showed 6 vs. die showed 1–5), compute the probability of your observation under each scenario, and then use those likelihoods to weight the prior probabilities. The key skill is identifying which events are conditional on which, and avoiding the common trap of confusing the direction of conditioning.

• Prior and posterior probabilities
• Likelihood and the law of total probability
• When and how to apply Bayes' rule