A question about Bayes' theorem

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In summary, the conversation is about a student answering a question on an American test with multiple choices. The question involves using Bayes' Theorem and conditional probability to determine the probability that the student studied the subject given that they answered correctly. The conversation also discusses analyzing the result for different values of m, which represents the number of options in the question.
  • #1
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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  • #2
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?
 

1. What is Bayes' theorem?

Bayes' theorem is a mathematical formula that describes the probability of an event based on prior knowledge or information.

2. Who developed Bayes' theorem?

Bayes' theorem was developed by Reverend Thomas Bayes, an English statistician, philosopher, and theologian, in the 18th century.

3. How is Bayes' theorem used in science?

Bayes' theorem is widely used in science, particularly in fields such as statistics, machine learning, and artificial intelligence, to update and revise probabilities based on new evidence or information.

4. Can you provide an example of how Bayes' theorem is used?

Sure! An example of Bayes' theorem in action is in medical diagnosis. A doctor may use Bayes' theorem to calculate the probability of a patient having a certain disease based on their symptoms and medical history.

5. What are the key components of Bayes' theorem?

Bayes' theorem consists of three key components: the prior probability (the initial belief or probability of an event occurring), the likelihood (the probability of obtaining certain evidence given the event has occurred), and the posterior probability (the updated belief or probability of the event occurring after taking into account the new evidence).

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