Guess and Check

What this Bayesian-reasoning interview question tests

This is an easy probability question that asks you to apply Bayes' theorem to update your belief about the source of an answer. It's a classic screening problem: given that Omar answered correctly, what is the probability he actually knew the answer versus got lucky?

To solve problems like this, you need to separate the prior probability (how likely Omar knows the answer in general) from the likelihood of observing a correct answer under each scenario. The key insight is recognizing that a correct answer could come from two different paths: knowledge or successful guessing. Firms use these questions to test whether you can structure conditional-probability reasoning and avoid the base-rate fallacy.

• Prior and posterior probabilities
• Bayes' theorem and belief updating
• Accounting for multiple causal paths to the same outcome