5.0 - Bayes’ Theorem
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Practice Questions
Test your understanding with targeted questions
What is the sample space?
💡 Hint: Think about all the outcomes of a dice roll.
What does P(A | B) represent?
💡 Hint: It's the probability of an event under certain conditions.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the prior probability represent in Bayes' Theorem?
💡 Hint: Consider the beliefs you have before receiving new information.
True or False: In Bayes' Theorem, the posterior probability is always greater than the prior probability.
💡 Hint: Reflect on the effect of evidence on beliefs.
1 more question available
Challenge Problems
Push your limits with advanced challenges
A rare condition affects 0.5% of the population. A screening test identifies the condition with 98% sensitivity and 90% specificity. Calculate the probability of having the condition given that a person tests positive.
💡 Hint: Remember to first derive P(T) using total probability.
A bag contains 10 blue and 20 red balls. You draw a ball at random and it’s red. What is the probability that the next drawn ball is red if you replace it?
💡 Hint: Think about the events being independent due to replacement.
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