Million-Dollar Wheel Spin Prob

This quant interview question is about understanding how information accumulates across independent stages in a probabilistic setting. You face a sequence of chances to gain perfect insight, and if they all fail, you fall back to a crude guess. It sits at the intersection of conditional probability, independence, and total probability, all classic themes in quant prep and trading interviews.

It trains your ability to decompose a stochastic process into clean, mutually exclusive scenarios and to track probabilities across them. You must be comfortable with independence, failure events, and a structured fallback mechanism. This is exactly the kind of thinking used in evaluating signals versus noise in trading strategies.

It matters for quant interviews because many real-world models have repeated noisy signals and occasional decisive information. Interviewers want to see that you can quantify success probabilities in such layered decision processes without getting lost in the narrative.

What it tests

When a process involves repeated independent trials, each with a chance to provide decisive information, the overall probability of success is best understood by partitioning into mutually exclusive cases: (1) at least one trial yields full information, guaranteeing success, and (2) all trials fail, forcing reliance on a fallback strategy. The total probability is then a weighted sum: the probability of decisive information plus the probability of fallback times its own success rate. This structure arises because independence allows us to multiply probabilities of joint failure, and the fallback is only relevant when all attempts fail. The key is that the process is dominated by the chance that at least one trial succeeds, not by the details of the fallback.