In answering on a multiple choice test, a student either know the answer or guesses. let p be the probability that the students knows the answer and 1-p be the probability that the student guesses. assume that a student who guesses at the answer will be correct with probability 1/m, where m is the number of multiple choice alternatives. what is the conditional probability that a student knew the answer to a question when he or she answered it correctly?

Step-by-step explanation:

For mutually exclusive events as A1, A2, A3, etc, Bayes' theorem states:

P(A|B) is a conditional probability: the likelihood of event A occurring given that B is true.

P(B|A) is a conditional probability: the likelihood of event B occurring given that A is true.

P(A) is the probability that A occurs

P(B) is the probability that B occurs

For this problem:

A1 is the probability that the student knows the answer

A2 is the probability that the student guesses the answer

B is the probability that the student answer correctly

P(B|A₁) means the probability that the answer is correct when he knew the answer

P(B|A₂) means the probability that the answer is correct when he guessed the answer

P(A₁|B) means the probability that he knew the answer when the answer was correct

Replacing everything in the Bayes' theorem you get:

astronomers is your final answer! : )

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step-by-step explanation: