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IB Maths AA HL Ahl 4 13 Hl Bayes Theorem Questions

Practise applying Bayes’ theorem to conditional-probability data, selecting the relevant events, calculating posterior probabilities and interpreting the result in context.

Syllabus
First assessment 2021
Course
Mathematics: analysis and approaches HL
Level
HL

Exam points

  • Use Bayes theorem to calculate a posterior probability from conditional probabilities and prior probabilities.
  • Represent diagnostic or population probability problems with a labelled tree, contingency table or equivalent conditional-probability structure.
  • Interpret false positives, false negatives and conditional probabilities in the context of testing or classification.

Learn this topic

Study AHL 4.13 (HL)—Bayes' theorem conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AA HL Ahl 4 13 Hl Bayes Theorem Questions question 1

[Maximum number: 3]

Amanda enters data from surveys into a database. It can be assumed that the accuracy of any survey entered is independent of all other surveys entered.
From previous records, it is known that Amanda enters 8 % of the surveys inaccurately.

Find the probability that a randomly selected survey was

entered by Amanda, given that the survey was entered inaccurately.

The following year, the accuracy of Amanda's and Bryce's work remained the same, as did the percentage of surveys entered by each of the three employees. However, Carmen's accuracy had improved and the probability that she entered a survey inaccurately was now x %.

The probability that a randomly selected survey had been entered inaccurately was now the same as the probability that Carmen made an error when entering a survey.

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