4.2.6 - Bayes’ Theorem
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Practice Questions
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Define Prior Probability in your own words.
💡 Hint: Think about how we estimate events before any new information impacts our beliefs.
What is meant by Posterior Probability?
💡 Hint: Relates to how our initial beliefs change with new data.
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Interactive Quizzes
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What does Bayes' Theorem help to revise?
💡 Hint: Think about the importance of integrating new facts.
True or False: Bayes' Theorem can only be applied in clinical research.
💡 Hint: Consider areas in which you make decisions based on probabilities.
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Challenge Problems
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In a rare disease, the probability of a test being positive given disease presence is 95%, but only 2% of the population has the disease. If tested positive, what is the probability actually having the disease?
💡 Hint: Be cautious of the prior probability being quite low compared to the false positives.
Suppose there's an 85% chance of rain if clouds are present. The prior probability that it rains is 40%. If clouds appear, what is the probability of it raining?
💡 Hint: Consider how presence of clouds correlate with rainfall.
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