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

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is a sample space?

💡 Hint: Think about what all can happen in an experiment.

Question 2

Easy

What does conditional probability represent?

💡 Hint: It involves two events and how they relate.

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 the formula for Bayes’ Theorem?

  • A) P(A|B) = P(B|A) * P(A) / P(B)
  • B) P(B|A) = P(A|B) * P(B) / P(A)
  • C) P(B|A) = P(A) + P(B)
  • D) P(A|B) = P(A) + P(B)

💡 Hint: Recall the components of the theorem.

Question 2

True or False: The posterior probability is the probability of an event after observing evidence.

  • True
  • False

💡 Hint: Think about how evidence influences our prior beliefs.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation