Find Expected Spins Until Two Regions Appear
Company: Sig
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
# Find Expected Spins Until Two Regions Appear
A spinner has three regions with landing probabilities `1/5`, `3/10`, and `1/2`. Spins are independent. Starting before the first spin, continue until the outcomes have included two distinct regions.
What is the expected total number of spins? Express the answer as a fraction in simplest form.
### What a Strong Answer Covers
- Recognition that the first spin always establishes the first observed region.
- Conditioning on which region appears first.
- A geometric waiting time whose success probability depends on that first region.
- Correct weighted averaging and fraction simplification.
### Follow-up Questions
- Which first region produces the longest expected remaining wait?
- How would you generalize the expression to any finite set of region probabilities?
Overview: Find the expected spins needed to observe two distinct regions on a nonuniform spinner. The solution conditions on the first region, applies a region-specific geometric waiting time, weights by the correct probabilities, and derives the reduced expectation 75/28.
Read the full Sig Data Scientist interview experience this question came from