Calculate conditional probability for user retention
Last updated: February 4, 2026
Quick Overview
Given the following scenario about revenue per session, calculate the the sample size needed.
Microsoft
Statistics & Math
Data Scientist
Microsoft
February 4, 2026Data Scientist
Take-home Project
Statistics & Math
Medium
34
4
4,730 solved
Given the following scenario about revenue per session, calculate the the sample size needed.
Microsoft values data-driven decision making. This Take-home Project question assesses whether you can design experiments, interpret results correctly, and avoid common statistical pitfalls like p-hacking or Simpson's paradox.
What the Interviewer Expects
- Set up the problem formally with proper notation
- Apply the correct statistical test with clear justification
- Interpret results with appropriate caveats and confidence levels
- Discuss practical significance vs statistical significance
- Identify potential confounders and how to address them
Key Topics to Cover
Conditional probability and Bayes theorem
Causal inference basics
Central Limit Theorem
Multiple testing correction (Bonferroni, FDR)
How to Approach This
- Define your hypotheses (H0 and H1) clearly before performing any test.
- Calculate required sample size BEFORE running an experiment, using power analysis.
- Remember the Central Limit Theorem: sample means become approximately normal with large n.
- Watch for Simpson's paradox. Always segment data by key dimensions.
- Distinguish between statistical significance and practical significance.
Possible Follow-up Questions
- How would you explain this result to a non-technical audience?
- What if the sample size is very small?
- What assumptions does this test make, and how would you validate them?
- What alternative statistical method could you use here?
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Browse Statistics QuestionsSample Answer
Problem Formulation
To evaluate user retention based on revenue per session, we need to define the following variables:
- Let be the event that a user generates revenue above a certain threshold during their ses...
Solution Approach
- Define the expected retention rate: Assume from previous data that (30% retention).
- Set a target for precision: We want our estimate of to be within ( \p...
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