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

Three students took the particular test. The professor comes and tells them only one has passed the…

Answered: Question 2: Three students took a test.…

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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In a certain class of 25 students, 12% received A’s, 30% received B’s, 42% received C’s, and 12% received D’s. How many students failed the class?
Three players enter a room and are given a red or a blue hat to wear. The color of each hat is determined by a fair coin toss. Players cannot see the color of their own hats, but do see the color of the other two players' hats. The game is won when at least one of the players correctly guesses the color of his own hat and no player gives an incorrect answer. In addition to having the opportunity to guess a color, players may also pass. Communication of any kind between players is not permissible after they have been given hats; however, they may agree on a group strategy beforehand. The players decided upon the following strategy. A player who sees that the other two players wear a hat with the same color guesses the opposite color for his/her own hat; otherwise, the player says nothing. What is the probability of winning the game under this strategy?
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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 profeesor ha shared the result for b
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