3 Prisoners

[The Truth]

There are three prisoners, you and Prisoners A and B. Two of you are to be executed, while one will be pardoned. The prison warden knows who will be executed and who will be pardoned (like monty must know where the goats and car are). According to policy, the warden is NOT allowed to tell any prisoner if he/she is to be pardoned. You point out to the warden that if he tells you if A or B will be executed, he will not be violating any rule. The warden says C is to be executed. What is the chance that you will be pardoned?


blake

p.s. forgive me if this has been posted before.

[New001]

<font color="white"> Still 1/3, isn't it? </font>

[MathEconomist]

This was posted in probability a couple of weeks ago. It is exactly the same as the monty hall problem, just another way of phrasing it.

[ElaineMonster]

Did you make a mistake? You said me and prisoners A and B. Warden says prisoner C will be executed. Am I prisoner C? Or did you make a mistake?

[The Truth]

I copied it directly from Winki, and yeah I think it was a mistake. I didn't notice it til now. It is supposed to be one of the other guys not you /images/graemlins/smile.gif

blake

[ElaineMonster]

<font color="white"> I think my chances of being pardonned are 2/3 </font>

[soon2bepro]

your chances of being pardoned are 0%, in the cell the 3 prisoners are identified as A, B and you. Since C isn't A or B (at least if we can assume that by common sense), C is you and you're to be executed

[soon2bepro]

[ QUOTE ]
I copied it directly from Winki, and yeah I think it was a mistake. I didn't notice it til now. It is supposed to be one of the other guys not you /images/graemlins/smile.gif

[/ QUOTE ]

in this case it's 50%. it is amazing that in this forum people are giving wrong answers to such an easy probability question

[New001]

[ QUOTE ]
[ QUOTE ]
I copied it directly from Winki, and yeah I think it was a mistake. I didn't notice it til now. It is supposed to be one of the other guys not you /images/graemlins/smile.gif

[/ QUOTE ]

in this case it's 50%. it is amazing that in this forum people are giving wrong answers to such an easy probability question

[/ QUOTE ]
Wikipedia: Monty Hall problem (http://en.wikipedia.org/wiki/Monty_Hall_problem)

[MathEconomist]

[ QUOTE ]
[ QUOTE ]
I copied it directly from Winki, and yeah I think it was a mistake. I didn't notice it til now. It is supposed to be one of the other guys not you /images/graemlins/smile.gif

[/ QUOTE ]

in this case it's 50%. it is amazing that in this forum people are giving wrong answers to such an easy probability question

[/ QUOTE ]

I really hope that's supposed to be a joke.

[maurile]

<font color="white">Let's change so that it makes sense: the warden says that B is to be executed.

From here it's a Bayes' theorem problem.

If you are going to be pardoned (prior = 1/3), the warden is 50% to say that A will be executed and 50% to say that B will be executed.

If B is going to be pardoned (prior = 1/3), the warden is 100% to say that A will be executed.

If A is going to be pardoned (prior = 1/3), the warden is 100% to say that B will be executed.

The warden says that B will be executed. So my chance at being pardoned is (1/3)(1/2)/[(1/3)(1/2)+(1/3)] = 1/3.</font>

[soon2bepro]

wow. you guys are right. it's 1/3 (no, it wasn't a joke)

[LadyWrestler]

[ QUOTE ]
There are three prisoners, you and Prisoners A and B. Two of you are to be executed, while one will be pardoned. The prison warden knows who will be executed and who will be pardoned (like monty must know where the goats and car are). According to policy, the warden is NOT allowed to tell any prisoner if he/she is to be pardoned. You point out to the warden that if he tells you if A or B will be executed, he will not be violating any rule. The warden says C is to be executed. What is the chance that you will be pardoned?


blake

p.s. forgive me if this has been posted before.

[/ QUOTE ]


<font color="white">0%, if he is telling the truth.</font>

Have a great day! /images/graemlins/smile.gif

[daryn]

how can you guys think that your original chances of being pardoned (33%) will be affected by what the warden says? he has to say something!
<font color="white"> i love these threads </font>

[soon2bepro]

yup you're right daryn

[daryn]

if you can.. switch! because of course, now the other guy has a 2/3 chance of being pardoned /images/graemlins/tongue.gif

[_TKO_]

[ QUOTE ]
This was posted in probability a couple of weeks ago. It is exactly the same as the monty hall problem, just another way of phrasing it.

[/ QUOTE ]

It's not the same; there is no option to switch.

In the Monty Hall problem, the chance that your current door will reveal a car is 1/3. The chance that the other door will reveal a car is 2/3.

In the 3 prisoners problem, the chance that you will be pardoned is 1/3. The chance that one of the other two prisoners will be pardoned is 2/3. With the given information, the chance that the other prisoner will be pardoned is 2/3. The chance that you will be pardoned is still 1/3.

[UnitBubble]

[ QUOTE ]
[ QUOTE ]
This was posted in probability a couple of weeks ago. It is exactly the same as the monty hall problem, just another way of phrasing it.

[/ QUOTE ]

It's not the same; there is no option to switch.

In the Monty Hall problem, the chance that your current door will reveal a car is 1/3. The chance that the other door will reveal a car is 2/3.

In the 3 prisoners problem, the chance that you will be pardoned is 1/3. The chance that one of the other two prisoners will be pardoned is 2/3. With the given information, the chance that the other prisoner will be pardoned is 2/3. The chance that you will be pardoned is still 1/3.

[/ QUOTE ]

Your lack of generalization will be your downfall.

[_TKO_]

[ QUOTE ]
Your lack of generalization will be your downfall.

[/ QUOTE ]
/images/graemlins/confused.gif

[UnitBubble]

OK fine. The whole game show thing with the switch or stay choices is just a word problem to "pretty up" the actual problem. Like "If I have three apples and then you steal one of my apples, how many apples do I have left?" is just a word problem to "pretty up" the expression 3-1.

[Borodog]

Actually the expression 3-1=2 "pretties up" a class of problems similar to "If I have three apples and then you steal one of my apples, how many apples do I have left?"

[UnitBubble]

That raises the whole "was math invented or discovered" argument, and apparently on that matter we disagree.

[Borodog]

I don't think it raises that argument at all. Rather, expressions like "3-1=2" are merely a shorthand, a notational simplification that represents, "If you remove one thing from three things, you are left with two things."

The axiomatic deductive nature of mathematics is independent of the particular notation one employs to simply the process.

[UnitBubble]

ohoh, I see what you mean now. You are right.

I didn't convey my ideas properly. Where I said "the expression 3-1" I should have said something like "the concept 3-1". Then, this argument would not have spawned.

[Borodog]

No problem.

Peace.