MHB A question about Bayes' theorem

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The 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. The problem involves calculating this probability based on the known likelihood of the student having studied (P) and the number of answer options (m). Participants are asked to express the theorem in conditional probability notation and analyze scenarios where m equals 1 and approaches infinity. The conversation emphasizes understanding the theorem's application in educational contexts and its implications for guessing versus knowledge. The thread aims to clarify the mathematical approach to these probability questions.
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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?
 

Thread 'A variant of the Monty Hall problem'

There is a nice little variation of the problem. The host says, after you have chosen the door, that you can change your guess, but to sweeten the deal, he says you can choose the two other doors, if you wish. This proposition is a no brainer, however before you are quick enough to accept it, the host opens one of the two doors and it is empty. In this version you really want to change your pick, but at the same time ask yourself is the host impartial and does that change anything. The host...
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