Sweet number 6

What this geometric-distribution interview question tests

This is a fundamental probability question that asks you to compute an expected value in a setting with repeated independent trials. It is commonly used as a warm-up or sanity-check problem in quant interviews to see whether you can set up and solve a classic geometric-distribution problem cleanly.

The question rewards clear reasoning about what "average" means in a probabilistic sense. You will need to define the random variable precisely (what counts as a "roll"?), set up the expectation, and solve it either by summing an infinite series, by using a recursive argument, or by invoking a known formula. Firms expect candidates to justify their setup and check that the answer is reasonable.

• Geometric distribution and its memoryless property
• Expected value of a sum of independent trials
• Algebraic manipulation of infinite series