probability question

[theben]

Heres the Q, not my own

Tom, Dick and Harry are in prison. One of them is scheduled to die in the morning, and the other two will be set free. Their guard knows which one will die, but none of the prisoners does. The guard is under strict instructions not to divulge the identity of the doomed man. Tom is desperate for any information beyond the fact that his odds of death are one in three. He begs the guard to throw him an informational bone. Finally, to shut him up, the guard agrees to reveal only the following: the name of one of Tom's fellow prisoners who will be set free rather than killed. The guard then says that Dick will be set free. After the guard's revelation, what is the probability that Tom will be killed?

a. 1/3
b. 1/2
c. 2/3
d. none of these

[hansdebelge]

b

[BruceZ]

[ QUOTE ]
Heres the Q, not my own

Tom, Dick and Harry are in prison. One of them is scheduled to die in the morning, and the other two will be set free. Their guard knows which one will die, but none of the prisoners does. The guard is under strict instructions not to divulge the identity of the doomed man. Tom is desperate for any information beyond the fact that his odds of death are one in three. He begs the guard to throw him an informational bone. Finally, to shut him up, the guard agrees to reveal only the following: the name of one of Tom's fellow prisoners who will be set free rather than killed. The guard then says that Dick will be set free. After the guard's revelation, what is the probability that Tom will be killed?

a. 1/3
b. 1/2
c. 2/3
d. none of these

[/ QUOTE ]

This is just Monty Hall in weak disguise, so of course the answer is a (assuming that the guard would have no compelling reason to reveal Dick over Harry were they both to be set free).

A better problem is that 2 prisoners out of 7 will be killed, and you being one of the prisoners asks the guard to reveal if you will be killed. The guard replies that he is not allowed to give you that information, but instead he identifies one of the other prisoners that will be killed. What is the probability that you will be killed?

[DWarrior]

Somewhere between (and including) 1/3 and 1/2, since the guard can be BSing.

[GTSamIAm]

1/2? Either Tom or Harry is going to die.

[GTSamIAm]

[ QUOTE ]
This is just Monty Hall in weak disguise, so of course the answer is a.

[/ QUOTE ]

What is Monty Hall? The chances of any person dying is one in three, and this decision is predetermined. If you can eliminate one person from dying, the two remaining must have an equal chance of death. So the two remaining must have a 1/2 chance of death each. How can the fact that the decision is predetermined override the new information the guard gives you?

[BettyBoopAA]

a
since one of the other two will always be set free, no info was actually obtained.

[BettyBoopAA]

2/7 for the better example

[BruceZ]

[ QUOTE ]

What is Monty Hall?

[/ QUOTE ]

That is described in the post "stupid 3-doors problem". See that one and my explanation. In that case, the question would allow Tom to trade places with Harry, which he should decline since Harry is twice as likely to die as Tom.


[ QUOTE ]
The chances of any person dying is one in three, and this decision is predetermined. If you can eliminate one person from dying, the two remaining must have an equal chance of death. So the two remaining must have a 1/2 chance of death each.

[/ QUOTE ]

That's where you're wrong. They do not have to be equal, and in fact they are not equal.

I didn't mean to engage myself in debate with people on this trivial problem which always gets tons of responses. Crap. /images/graemlins/ooo.gif

[BruceZ]

[ QUOTE ]
a
since one of the other two will always be set free, no info was actually obtained.

[/ QUOTE ]

The answer is a, but info was obtained about Harry's chances. Since Tom's probability stayed at 1/3, Harry's changed from 1/3 to 2/3.