Calculate Conversion Probability for Male Ad Impressions

Q: Calculate Conversion Probability for Male Ad Impressions

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.

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Question

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.

Calculate Conversion Probability for Male Ad Impressions

Scenario

Given

Tasks

Solution

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