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

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does the term 'prior probability' refer to?

💡 Hint: Think about what you believe before you get new data.

Question 2

Easy

In the example problem, what is the false positive rate?

💡 Hint: It's the rate at which those without the disease test positive.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is Bayes' Theorem primarily used for?

  • Calculating averages
  • Updating probabilities
  • Finding probabilities of independent events

💡 Hint: Recall the purpose of the theorem.

Question 2

True or False: The false positive rate represents the probability of testing negative when the disease is present.

  • True
  • False

💡 Hint: Understand what false positive means.

Solve 3 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation