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

Practice: Summary

Lesson 5.X.XBayes’ Theorem

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9 questions

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4 cards from this section. Quick, good the night before a test.
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6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is a sample space?
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Think about what all can happen in an experiment.
Question 2.
What does conditional probability represent?
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It involves two events and how they relate.
3Question 3.
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)
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Recall the components of the theorem.
4Question 4.
True or False: The posterior probability is the probability of an event after observing evidence.
- True
- False
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Think about how evidence influences our prior beliefs.
Question 5.
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.
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Carefully analyze the components of Bayes' Theorem, paying attention to each probability involved.
Question 6.
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?
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Refer to previously covered definitions and remember to plug in values methodically into Bayes' Theorem.

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