5.X.2 - Statement of Bayes’ Theorem
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Practice Questions
Test your understanding with targeted questions
What is Bayes' Theorem used for?
💡 Hint: Think about how we revise our guesses when we get more information.
What is the formula for Bayes’ Theorem?
💡 Hint: Remember the structure: Posterior is influenced by Likelihood.
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Interactive Quizzes
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What does Bayes' Theorem calculate?
💡 Hint: Think about how we adjust our beliefs with new findings.
True or False: Bayes' Theorem can be used in machine learning.
💡 Hint: Consider the contexts where probabilistic models are applied.
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Challenge Problems
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A clinical test has a 90% sensitivity and 80% specificity. The disease prevalence is 5%. How would you compute the probability of actually having the disease after a positive test result?
💡 Hint: Ensure you factor in the specificity for false positives.
In a machine learning context, if a certain algorithm predicts a class with 85% accuracy, and the class prevalence is 30%, what would be the posterior probability of the class given a positive prediction?
💡 Hint: Break down accuracy into its components to understand true positives vs. false positives.
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