What is the probability that professor will be found in the fifth classroom?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 50E: Medicine Out of a group of 9 patients treated with a new drug, 4 suffered a relapse. Find the...
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A student is looking for a professor at the university. The professor is with equal probability in one of the 5 classrooms, and the probability that he is at the faculty at all is p. The student already checked 4 classrooms and did not find the professor. What is the probability that professor will be found in the fifth classroom?

 

 

 

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Follow-up Question

Let Hi be the event that the professor is in the ith classroom

p(H1)=p(H2)=p(H3)=p(H4)=p(H5)=1/5

A-event that the professor is at the faculty, p(A)=p

B-event that the professor is not at the faculty, p(B)=1-p

It is necessary to find the probability p(H5|H4`H3`H2`H1`), i.e. the probability that the student will find the professor in the fifth classroom, provided that he did not find him in the previous 4

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Follow-up Question

I think that the solution is not good, because it is a matter of conditional probability and the Bayesian formula. It is necessary to first calculate the probability that the student did not find the professor in the first 4 classrooms, and only on that basis calculate the probability that he will find him in the fifth.

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