The Magic Wheel

What this conditional probability interview question tests

This is an easy probability question that probes your ability to reason about sequential events and conditional outcomes. It asks you to think through what happens when you gather (or fail to gather) information, and how that shapes your final odds of success.

The core skill is setting up the problem correctly: identifying the sample space, computing the probability of different information states after multiple trials, and then calculating your winning probability given those states. Firms ask questions like this to see whether you can break a multi-step scenario into clear stages and combine probabilities without getting lost.

• Compound probability and the multiplication rule
• Reasoning about information and its absence
• Conditional probability and the law of total probability
• Fallback strategies (random guessing) when information fails