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The "prisoner's dilemma". Three prisoners, Tom, Dick, and Harry, are in solitary confinement on Death Row. Under a general amnesty, two of them – chosen at random – are to be released. The prison governor calls Tom into his office, and says: "I am not allowed to tell you yet whether you will be released; but I can, if you like, give you the name of one of the others who will definitely be released". Should Tom allow his curiosity to get the better of him, with the following reasoning? His chances of being released are initially 2/3; but, as soon as he knows that, say, Harry is to be released, his odds drop instantly to 50/50 since either he or Dick must then be executed. Use Bayes' theorem to demonstrate the flaw in this reasoning.

The "prisoner's dilemma". Three prisoners, Tom, Dick, and Harry, are in solitary confinement on Death Row. Under a general amnesty, two of them – chosen at random – are to be released. The prison governor calls Tom into his office, and says: "I am not allowed to tell you yet whether you will be released; but I can, if you like, give you the name of one of the others who will definitely be released". Should Tom allow his curiosity to get the better of him, with the following reasoning? His chances of being released are initially 2/3; but, as soon as he knows that, say, Harry is to be released, his odds drop instantly to 50/50 since either he or Dick must then be executed. Use Bayes' theorem to demonstrate the flaw in this reasoning.

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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The "prisoner's dilemma". Three prisoners, Tom, Dick, and Harry, are in solitary confinement on Death Row. Under a general amnesty, two of them – chosen at random – are to be released. The prison governor calls Tom into his office, and says: "I am not allowed to tell you yet whether you will be released; but I can, if you like, give you the name of one of the others who will definitely be released". Should Tom allow his curiosity to get the better of him, with the following reasoning? His chances of being released are initially 2/3; but, as soon as he knows that, say, Harry is to be released, his odds drop instantly to 50/50 since either he or Dick must then be executed. Use Bayes' theorem to demonstrate the flaw in this reasoning.
Transcribed Image Text:The "prisoner's dilemma". Three prisoners, Tom, Dick, and Harry, are in solitary confinement on Death Row. Under a general amnesty, two of them – chosen at random – are to be released. The prison governor calls Tom into his office, and says: "I am not allowed to tell you yet whether you will be released; but I can, if you like, give you the name of one of the others who will definitely be released". Should Tom allow his curiosity to get the better of him, with the following reasoning? His chances of being released are initially 2/3; but, as soon as he knows that, say, Harry is to be released, his odds drop instantly to 50/50 since either he or Dick must then be executed. Use Bayes' theorem to demonstrate the flaw in this reasoning.
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