A question about Bayes' theorem

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SUMMARY

This discussion centers on applying Bayes' Theorem to determine the probability that a student studied a subject given a correct answer on a multiple-choice test with m options. The problem is framed with a known probability P that the student has learned the material. The two parts of the question require calculating the conditional probability and analyzing the outcomes for m=1 and as m approaches infinity. The conversation also touches on the notation used in conditional probability.

PREREQUISITES
  • Understanding of Bayes' Theorem
  • Familiarity with conditional probability notation
  • Basic knowledge of probability concepts
  • Experience with multiple-choice testing scenarios
NEXT STEPS
  • Study the derivation of Bayes' Theorem in detail
  • Explore examples of conditional probability calculations
  • Analyze the implications of varying m in multiple-choice questions
  • Learn about common applications of Bayes' Theorem in real-world scenarios
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Students, educators, and data analysts interested in probability theory, particularly those looking to apply Bayes' Theorem in educational assessments or statistical analysis.

lola19991
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I would like to know how to solve the following question:

A student answers a question in American test that has m options that are given as follows:
In probability P the student has learned the question and therefore knows how to choose the correct answer, otherwise he guesses the question.
a) What is the probability that the student studied the subject of the question given that he answered correct on the question?
b) Analyze the result for m=1 and m->inf
 
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lola19991 said:
I would like to know how to solve the following question:

A student answers a question in American test that has m options that are given as follows:
In probability P the student has learned the question and therefore knows how to choose the correct answer, otherwise he guesses the question.
a) What is the probability that the student studied the subject of the question given that he answered correct on the question?
b) Analyze the result for m=1 and m->inf

Hi lola9991,

How would you explain or write Bayes' Theorem to start? How would you write A in conditional probability notation?
 

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