Calculate Posterior Probability Using Bayes' Theorem Example

Q: Calculate Posterior Probability Using Bayes' Theorem Example

This question evaluates understanding of Bayes' theorem and probabilistic reasoning for computing posterior probabilities in binary classification, emphasizing priors, likelihoods, and conditional probability.

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Question

Bayes' Theorem Toy Problem: Spam-Flag Example

Context

You are evaluating a simple classifier that flags messages as spam. Based on historical data, you know the spam rate and the classifier’s performance (true positive and false positive rates). Compute the probability that a message is truly spam given it was flagged.

Assume:

Prior spam rate: 2% of all messages are spam.
If a message is spam, the classifier flags it 90% of the time.
If a message is not spam, the classifier still flags it 5% of the time (false positive).

Task

Walk through a complete Bayes-theorem calculation:

Clearly define the prior P(H) and likelihoods P(E|H), P(E|¬H).
Write the full formula.
Compute the posterior P(H|E) and report the final numeric answer.

Show every step, state assumptions, and simplify the final answer to a clear fraction and a one-decimal percentage.

Calculate Posterior Probability Using Bayes' Theorem Example

Bayes' Theorem Toy Problem: Spam-Flag Example

Context

Task

Solution

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