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Question 2: Three students took a test. The professor comes and tells them that only one has passed the test. "Which is it?" they ask. "I can't tell you that," says the professor. "I can't tell a student their own fate before the results are declared." Student A takes the professor aside. "Look," he says. "Of the three of us, only one has passed. That means that one of my fellow students is still sure to fail. Give me his name. That way you're not telling me my own fate." The guard thinks about this and tells him, "Student B has failed." Student A rejoices that his own chances of passing have improved from 1/3 to 1/2. But how is this possible? The professor has given him no new information. Or has he? What do you think? Has the chances of student A risen from 1/3 to 1/2 and if so, why? Or does it still remain at 1/3 and if so, why? Can you specify what the initial chances were of each student passing/failing, and what their chances are after the professor has shared the results for student B? Note that student C doesn't know anything about this conversation - has her chances changed too?

Question 2: Three students took a test. The professor comes and tells them that only one has passed the test. "Which is it?" they ask. "I can't tell you that," says the professor. "I can't tell a student their own fate before the results are declared." Student A takes the professor aside. "Look," he says. "Of the three of us, only one has passed. That means that one of my fellow students is still sure to fail. Give me his name. That way you're not telling me my own fate." The guard thinks about this and tells him, "Student B has failed." Student A rejoices that his own chances of passing have improved from 1/3 to 1/2. But how is this possible? The professor has given him no new information. Or has he? What do you think? Has the chances of student A risen from 1/3 to 1/2 and if so, why? Or does it still remain at 1/3 and if so, why? Can you specify what the initial chances were of each student passing/failing, and what their chances are after the professor has shared the results for student B? Note that student C doesn't know anything about this conversation - has her chances changed too?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question 2: Three students took a test. The professor comes and tells them that only one has passed the test. "Which is it?" they ask. “I can't tell you that," says the professor. “I can't tell a student their own fate before the results are declared." Student A takes the professor aside. "Look," he says. "Of the three of us, only one has passed. That means that one of my fellow students is still sure to fail. Give me his name. That way you're not telling me my own fate." The guard thinks about this and tells him, “Student B has failed." Student A rejoices that his own chances of passing have improved from 1/3 to 1/2. But how is this possible? The professor has given him no new information. Or has he? What do you think? Has the chances of student A risen from 1/3 to 1/2 and if so, why? Or does it still remain at 1/3 and if so, why? Can you specify what the initial chances were of each student passing/failing, and what their chances are after the professor has shared the results for student B? Note that student C doesn't know anything about this conversation - has her chances changed too?
Transcribed Image Text:Question 2: Three students took a test. The professor comes and tells them that only one has passed the test. "Which is it?" they ask. “I can't tell you that," says the professor. “I can't tell a student their own fate before the results are declared." Student A takes the professor aside. "Look," he says. "Of the three of us, only one has passed. That means that one of my fellow students is still sure to fail. Give me his name. That way you're not telling me my own fate." The guard thinks about this and tells him, “Student B has failed." Student A rejoices that his own chances of passing have improved from 1/3 to 1/2. But how is this possible? The professor has given him no new information. Or has he? What do you think? Has the chances of student A risen from 1/3 to 1/2 and if so, why? Or does it still remain at 1/3 and if so, why? Can you specify what the initial chances were of each student passing/failing, and what their chances are after the professor has shared the results for student B? Note that student C doesn't know anything about this conversation - has her chances changed too?
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