5.X.X - Summary
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Practice Questions
Test your understanding with targeted questions
What is a sample space?
💡 Hint: Think about what all can happen in an experiment.
What does conditional probability represent?
💡 Hint: It involves two events and how they relate.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the formula for Bayes’ Theorem?
💡 Hint: Recall the components of the theorem.
True or False: The posterior probability is the probability of an event after observing evidence.
💡 Hint: Think about how evidence influences our prior beliefs.
1 more question available
Challenge Problems
Push your limits with advanced challenges
A certain type of rare cancer affects 0.1% of the population. A new test has a 95% sensitivity and a 10% false positive rate. Calculate the probability that a person has cancer given they tested positive.
💡 Hint: Carefully analyze the components of Bayes' Theorem, paying attention to each probability involved.
During an investigation, a witness claims to have seen a suspect at the crime scene. If there's only a 5% chance the witness is correct and this suspect has a prior probability of guilt of 20%, what is the updated probability of guilt if the evidence points to him?
💡 Hint: Refer to previously covered definitions and remember to plug in values methodically into Bayes' Theorem.
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