5.X.5 - Example Problem
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Practice Questions
Test your understanding with targeted questions
What does the term 'prior probability' refer to?
💡 Hint: Think about what you believe before you get new data.
In the example problem, what is the false positive rate?
💡 Hint: It's the rate at which those without the disease test positive.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is Bayes' Theorem primarily used for?
💡 Hint: Recall the purpose of the theorem.
True or False: The false positive rate represents the probability of testing negative when the disease is present.
💡 Hint: Understand what false positive means.
3 more questions available
Challenge Problems
Push your limits with advanced challenges
A screening test for a particular cancer is 90% sensitive (true positive rate) and 85% specific (true negative rate). If the prevalence of the cancer in the population is 0.05, calculate the probability that a person has cancer given a positive test result.
💡 Hint: Break down the known probabilities and apply Bayes' formula.
A new survey finds that 2% of a population has a particular disease. If a diagnostic test identifies it with a true positive rate of 88% and a false positive rate of 7%, determine the probability that someone has the disease after testing positive.
💡 Hint: Use the known rates for true and false conditions to compute the posterior probability.
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