Estimate free-trial conversion probability
Company: IBM
Role: Data Scientist
Category: Analytics & Experimentation
Difficulty: easy
Interview Round: Technical Screen
## Context
A product offers a **free trial**. You are asked: “What is the probability of conversion for a group of people who started a free trial?”
## Data (assume available)
A table of trial starts:
- `user_id`
- `trial_start_at` (timestamp)
- `trial_length_days` (int)
- `country/channel/plan/device` (optional segments)
A table of paid conversions:
- `user_id`
- `paid_start_at` (timestamp, nullable if never converted)
- `revenue` (optional)
## Task
1. Define precisely what “conversion probability” means, including the **time window** and cohort definition.
2. Show how you would estimate the conversion probability for a cohort of trial starters, including how you would handle:
- users whose trial has not ended yet (incomplete observation)
- delayed conversions (convert after trial)
- segmentation and potential confounding (e.g., channel mix changes)
3. Provide a way to quantify uncertainty (confidence/credible intervals) and communicate results.
4. Suggest follow-up analyses/metrics (diagnostics and guardrails) to ensure the estimate is decision-useful.
Overview: This question evaluates a data scientist's competency in cohort definition, censored-data handling, segmentation and confounding assessment, and uncertainty quantification for measuring free-trial to paid conversion, and it belongs to the Analytics & Experimentation domain within data science.
Read the full IBM Data Scientist interview experience this question came from