Practice Example Problem (5.X.5) - Bayes’ Theorem - Mathematics - iii (Differential Calculus) - Vol 3

Practice: Example Problem

Lesson 5.X.5Bayes’ Theorem

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11 questions

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6 sample questions

Question 1.
What does the term 'prior probability' refer to?
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Think about what you believe before you get new data.
Question 2.
In the example problem, what is the false positive rate?
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It's the rate at which those without the disease test positive.
3Question 3.
What is Bayes' Theorem primarily used for?
- Calculating averages
- Updating probabilities
- Finding probabilities of independent events
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Recall the purpose of the theorem.
4Question 4.
True or False: The false positive rate represents the probability of testing negative when the disease is present.
- True
- False
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Understand what false positive means.
Question 5.
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.
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Break down the known probabilities and apply Bayes' formula.
Question 6.
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.
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Use the known rates for true and false conditions to compute the posterior probability.

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