Practice Bayes’ Theorem – Complete Detail - 5.X | 5. Bayes’ Theorem | Mathematics - iii (Differential Calculus) - Vol 3
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5.X - Bayes’ Theorem – Complete Detail

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the definition of sample space?

💡 Hint: Think about all things that can happen in a probability experiment.

Question 2

Easy

Explain conditional probability using the notation P(A|B).

💡 Hint: Focus on what is known when B happens.

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?

  • To measure central tendency
  • To update probabilities based on evidence
  • To calculate variance

💡 Hint: Think about how you adjust your beliefs when new information comes.

Question 2

True or False: The posterior probability is the same as the prior probability.

  • True
  • False

💡 Hint: Recall the definitions of prior and posterior.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

A factory produces two types of items: A and B. Items A have a defect rate of 5%, while items B have a defect rate of 10%. If 70% of items produced are of type A, what is the probability that a randomly selected defective item came from type B?

💡 Hint: Consider applying the theorem with both defect rates and prior production proportions.

Question 2

In a clinical trial, a med shows a 90% treatment response rate. However, 15% of non-responders still show improvement due to external factors. How is this scenario modeled using Bayes’ Theorem to assign probabilities upon observing a response?

💡 Hint: Survey how patient responses lead to refined probabilities regarding treatment efficacy.

Challenge and get performance evaluation