5.X.3 - Derivation of Bayes’ Theorem
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Practice Questions
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Define sample space.
💡 Hint: Think of what you would observe.
What does conditional probability measure?
💡 Hint: It involves two events.
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Interactive Quizzes
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What is Bayes' Theorem used for?
💡 Hint: Think about updating beliefs.
True or False: The prior probability changes when new evidence is introduced.
💡 Hint: What does 'prior' mean?
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Challenge Problems
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A factory produces 5% defective items. An inspection process has an 80% success rate in detecting defects. If an item is inspected and found defective, what is the probability that it is actually defective?
💡 Hint: Work through joint probabilities and apply Bayes' Theorem carefully.
In clinical trials, a new drug shows efficacy in 70% of patients. There is a 10% chance of side effects. If side effects occur, what's the updated probability that the patient benefited from the drug?
💡 Hint: Set up your known probabilities and use Bayes' formula.
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