An interesting problem

[iago]

I'm adapting this from a problem we discussed in my Machine Learning class to match a problem posted by Newby:

There is a table with 3 guns.  Two of them are loaded, one isn't.  You have no way of telling which one is loaded.  A man tells you he will kill you unless you pick up one of the guns and shoot yourself in the head.  If the gun is loaded (66%), you die.  If the gun isn't (33%) you get to walk out and go home.

The man asks you which gun, 1, 2, or 3.  You choose gun 2.  He picks up gun 3, and shoots the ceiling (it's loaded).  At this point, he asks you if you would like to change your mind and pick gun 1.

The question is: should you change your mind? What are the odds that gun 2 is loaded? What are the odds that gun 1 is loaded?

[Mythix]

The question is: should you change your mind? What are the odds that gun 2 is loaded? What are the odds that gun 1 is loaded?

50%!


Go for it.

Also if the gun you choose point it at the guy threatening to kill you, if it shoots you win, if it doesn't just say "haha I got you, I knew it wasn't loaded!"

[iago]

The question is: should you change your mind? What are the odds that gun 2 is loaded? What are the odds that gun 1 is loaded?

50%!

Wrong!  And you didn't answer all my questions, but 50% isn't correct for any of them.

[truste1]

No. 33%. 33%.

[iago]

No. 33%. 33%.

No.  Because you have already eliminated gun 3 as being the unloaded gun.

[Quik]

1 out of 2 that the gun is loaded. Same with first gun.

[iago]

1 out of 2 that the gun is loaded. Same with first gun.

Nope.

[truste1]

No. 33%. 33%.

No.  Because you have already eliminated gun 3 as being the unloaded gun.

No, you're wrong:

He picks up gun 3, and shoots the ceiling (it's loaded).

Right there you said gun 3 is loaded. Nowhere in your post did you say that there is only one bullet in the gun, so it's safe to assume that there is still more bullets in the gun. Hence the reason I said 33%, no gun has been eliminated as being unloaded.

But it doesn't matter anyway, 

... pick up one of the guns and shoot yourself in the head.

- you're required to shoot yourself in the head, not just attempt to shoot yourself in the head. Sucks.

[iago]

The presumption is that when he shows you that Gun 3 is loaded, that elimates Gun 3 (it's thrown out the window or something).

Anyway, the answer is this:
Gun 1 (the gun you initially chose) - 33% that you're safe -- there were 3 guns to choose from, and you had a 1/3 of getting the right one.
Gun 2 - 66% that you're safe -- the easiest way to picture this is to think that gun 1 is 33% (that should be obvious), and the other gun has the inverted chance, since you know Gun 3 can't be the right one.

We actually drew out the full tree (which gun, which had no bullet, and which you chose) in class to prove it; you can draw it yourself if you don't believe me.

[truste1]

I'm still certain that, given my justification, my answer was correct.

[iago]

I'm still certain that, given my justification, my answer was correct.

Yes, but your justification was wrong.

If A implies B (A -> B), and A is false, then B is irrelevant :P

[truste1]

You didn't give adequate details.