Calculate Conversion Probability for Male Ad Impressions
Overview
This question evaluates understanding of conditional probability and Bayesian inference, including interpretation of marginal and conditional conversion rates and the use of the law of total probability and Bayes' rule.
Meta
Aug 4, 2025, 10:55 AM
Data Scientist
Onsite
Statistics & Math
18
0
Scenario
You are estimating conversion probabilities for ad impressions. Before knowing a user's gender, the overall conversion rate is 2%.
Given
- P(convert) = 2%
- P(convert | male) = 3%
- P(convert | female) = 1%
Tasks
- After observing the user is male, what is the updated conversion probability? Explain the formula you used.
- If an ad converts, what is the probability the user is male? Show your steps using the law of total probability and Bayes’ rule.
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