4.3.6 - Bayes’ Theorem
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Practice Questions
Test your understanding with targeted questions
What does Bayes' Theorem help you update?
💡 Hint: Think about how new information affects your predictions.
Define prior probability.
💡 Hint: What was your initial belief before learning new information?
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Interactive Quizzes
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What does Bayes' Theorem allow us to do?
💡 Hint: Consider what this theorem is used for in real-life situations.
True or False: The prior probability is adjusted after receiving new evidence.
💡 Hint: Recall what prior means and when it is set.
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Challenge Problems
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In a study, a certain disease has a prevalence of 2% in the population. If a test for the disease has a true positive rate of 85% and a false positive rate of 10%, calculate the probability that a person who tests positive actually has the disease.
💡 Hint: Break it down step-by-step and remember to calculate overall testing probability.
A new drug shows a positive effect in 90% of patients with a certain condition, but only in 5% of healthy patients. If 10% of the population has the condition, calculate the probability that someone who responds positively to the drug actually has the condition.
💡 Hint: Ensure to track the overall probability via the entire population.
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