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Originally posted by Galileo in the thread I started called Bad Math Jokes on top of pg. 4:
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Not so much a joke as a brainteaser.
Three prisoners, strangers to each other, were suspects of a murder case. One day they came to hear that a sentence has been drawn. Two of them have been found guilty and will be executed, but they don't know which of the two . One guy, a statistician, figures his chances for survival are 1/3, so he goes to the bars of his cell and hails the guard: "Hey psst, do you know which of us has been sentenced?".
"Eh, yes.", says the guard, "But I'm not allowed to tell you.".
"Tell you what", says the guy, "I already know that 2 of us will executed, that means at least one of the other guys will be. I don't know them or anything, surely you can point to one which is guilty?". The guard sees no harm in that and points one of the prisoners, "He is guilty".
"Thanks!", proclaims the statistician, "my chances have just increased to 1/2".
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If you've got the time, throughout the next several pages of the original thread linked above starting on pg. 4 there are varying analyses of this 'brainteaser' (that do not all agree) and I felt after reading every relevant post on this that we hadn't really gotten to the bottom of it, or clearly I did not understand it if we did for I am left wanting a convincing analysis. Please explain, citing any formulae beyond the basics: I have taken an elementary probability and statistics course, and I know some analysis if need be.
Thanks for your time,
-Ben Orin
_____________________________________________________________________________________________________________________
Not so much a joke as a brainteaser.
Three prisoners, strangers to each other, were suspects of a murder case. One day they came to hear that a sentence has been drawn. Two of them have been found guilty and will be executed, but they don't know which of the two . One guy, a statistician, figures his chances for survival are 1/3, so he goes to the bars of his cell and hails the guard: "Hey psst, do you know which of us has been sentenced?".
"Eh, yes.", says the guard, "But I'm not allowed to tell you.".
"Tell you what", says the guy, "I already know that 2 of us will executed, that means at least one of the other guys will be. I don't know them or anything, surely you can point to one which is guilty?". The guard sees no harm in that and points one of the prisoners, "He is guilty".
"Thanks!", proclaims the statistician, "my chances have just increased to 1/2".
_____________________________________________________________________________________________________________________
If you've got the time, throughout the next several pages of the original thread linked above starting on pg. 4 there are varying analyses of this 'brainteaser' (that do not all agree) and I felt after reading every relevant post on this that we hadn't really gotten to the bottom of it, or clearly I did not understand it if we did for I am left wanting a convincing analysis. Please explain, citing any formulae beyond the basics: I have taken an elementary probability and statistics course, and I know some analysis if need be.
Thanks for your time,
-Ben Orin