Need a High Roll

What this dice-rolling expected-value question tests

This is an easy probability question that asks you to compute the expected sum across a sequence of rolls that ends under a stopping condition. It's a classic warm-up for probability interviews at quant trading and finance firms, testing whether you can set up and solve a straightforward expectation problem.

The key insight is recognizing that the stopping condition (rolling above a threshold) partitions the problem into two parts: rolls that don't meet it, and the final roll that does. You'll need to think carefully about how the expected value of each part contributes to the total, and how many rolls you expect to make before stopping.

• Expectation of a sum and linearity of expectation
• Geometric distributions and expected stopping times
• Conditional reasoning about the final roll