Keep spinning!

What this stopping-time expectation question tests

This is a medium-difficulty probability question that asks you to find the expected number of spins until a stopping condition is met. Quant firms use problems like this to assess whether you can set up and solve expectation equations under a non-uniform distribution, and whether you think clearly about when a process terminates.

The key challenge is recognizing that the stopping time depends on which regions you've already visited, so you need to condition on the state of the process (how many distinct regions seen so far) and use the law of total expectation to write a system of equations. The unequal probabilities add a small layer of care to the arithmetic.

• Stopping times and first-passage problems
• Conditioning and state-based recursion
• Law of total expectation with non-uniform distributions
• Solving linear equations in expectation