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  #21  
Old 01-15-2005, 02:55 AM
dtbog dtbog is offline
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Default Re: A Microsoft Interview Question (aka basic Bayes\' Theorem)

[ QUOTE ]
I know - it was a joke (or an attempt at one).

[/ QUOTE ]

Then the answer is "don't spin, just clean up all of the brains on the floor and then run like hell!"

-DB
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  #22  
Old 01-15-2005, 02:56 AM
VBM VBM is offline
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Default Re: A Microsoft Interview Question (aka basic Bayes\' Theorem)

ok, feeling dumb...i get it now...and i think you guys dont' wanna get into a russian roulette game w/ me now!!! lol...
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  #23  
Old 01-15-2005, 03:11 AM
RJT RJT is offline
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Default Re: A Microsoft Interview Question (aka basic Bayes\' Theorem)

[ QUOTE ]
[ QUOTE ]
I know - it was a joke (or an attempt at one).

[/ QUOTE ]

Then the answer is "don't spin, just clean up all of the brains on the floor and then run like hell!"

-DB

[/ QUOTE ]

See things aren't always so obvious. At first we both thought the answer was to spin after he shot himself. Now that you say it - the answer is to not spin and get the heck out of there. I am not quite sure of your logic regarding cleaning up the brains, though. Nite bud.
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  #24  
Old 01-15-2005, 04:12 AM
pzhon pzhon is offline
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Default Re: A Microsoft Interview Question (aka basic Bayes\' Theorem)

[ QUOTE ]
[ QUOTE ]
Had he shot himself, are you better off spinning or not?

[/ QUOTE ]

For the love of God, spin! [img]/images/graemlins/smile.gif[/img]

If he shot himself, you're 50/50 to die.


[/ QUOTE ]
Though this variant can be understood by considering two simple cases, it isn't easier than the original. The 1/3 chance to die from from spinning is the weighted average of this 1/2 and the probability from the original question, firing after the first chamber was empty. Since 1/2 is greater than 1/3, the chance to die from firing without spinning (1/4) must be less than 1/3.
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  #25  
Old 01-15-2005, 04:16 AM
Marm Marm is offline
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Default Re: A Microsoft Interview Question (aka basic Bayes\' Theorem)

Actually, that helped me understamd the 'states' end of the problem. Thanks.

Been up a long time, i'm moving slow......
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  #26  
Old 01-15-2005, 04:18 AM
Marm Marm is offline
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Default Re: A Microsoft Interview Question (aka basic Bayes\' Theorem)

Wrong, You are 50/50 to die if you don't spin, but spinning has only a 1/6 chance of dieing now, since one of the roudns has been fired, and can now be considered empty.

But I agree, leaving is the best idea.
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  #27  
Old 01-15-2005, 04:26 AM
JoshuaD JoshuaD is offline
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Default Re: A Microsoft Interview Question (aka basic Bayes\' Theorem)

there are 4 pairings that start with a blank hole, we're on one of those. 1 of those pairings will kill me, so it's 1/4 to die if I don't spin, and 1/3 to die if I do.

That said, what happens if I shoot a blank? No one's looking past step one (I haven't yet either, so we could end up w/ the same result, I just think it's interesting):

So my chance of getting blown away with

No Re-spin: 1/4 - 3/4 * 1/3 + 1/4 * 1/6 = 1/18
Re-Spin: 1/3 - 1/9 + 1/27 - 1/81... = 1/2


So you should definitely, definitely re-spin.

edit: this math is wrong, fixing.
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  #28  
Old 01-15-2005, 05:01 AM
pzhon pzhon is offline
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Default Re: A Microsoft Interview Question (aka basic Bayes\' Theorem)

[ QUOTE ]
Wrong, You are 50/50 to die if you don't spin, but spinning has only a 1/6 chance of dieing now, since one of the roudns has been fired, and can now be considered empty.


[/ QUOTE ]
Thank you for pointing out that triviality for those who missed it. However, when I said "The 1/3 chance to die from spinning..." I still referred to the original situation, spinning with 2 bullets in the gun.

[ QUOTE ]

But I agree, leaving is the best idea.

[/ QUOTE ]
That wasn't my point at all. I pointed out that the two variants must have probabilities differing from 1/3 in opposite directions. That is not trivial.
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  #29  
Old 01-15-2005, 05:22 AM
Supern Supern is offline
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Default Without reading any other answers

If you spin you have 4 chambers without a round and
2 with a round. You have 4/6 to survive when you pull the trigger.

When you just have pushed the trigger:
There are 4 empty chambers. Lets name them 1-4.
If he clicked chambers 1-3 you will get an empty chamber.
If he clicked chamber 4 you are in trouble. [img]/images/graemlins/smile.gif[/img]
That means you will survive 3/4 times.

The conclusion is: just pull the trigger (75% > 66%)
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  #30  
Old 01-15-2005, 05:58 AM
JoshuaD JoshuaD is offline
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Default Re: A Microsoft Interview Question (aka basic Bayes\' Theorem)

Alright, my math up above was all done in my head, and was wrong. Here's the actual right answer:

Assuming every previous shot is a blank, here are the chances on each round of getting blown away:

1) 1/3
2) 1/4
3) 1/3
4) 1/2
5) 1

HOWEVER, this answer suggests flawed results:

If we don't assume every previous shot is a blank, here are the chances of the person getting blown away on each round if there is never a respin, (That is, you're at round one, what are the chances of the gun going off on each round).

1) 1/3
2) 2/3 * 1/4 = 1/6
3) 2/3 * 3/4 * 1/3 = 1/6
4) 2/3 * 3/4 * 2/3 * 1/2 = 1/6
5) 2/3 * 3/4 * 2/3 * 1/2 = 1/6

So, if you're firing on all even rounds, and he's firing on all odd rounds, you get blown away 1/3 of the time, he gets blown away 2/3 of the time. So handing him the gun first was definitely a good idea.

However, if you assume he already shot the first round and he missed, AND if there is never a re-spin, the chances of the gun going off in each round is:

1) 0 < (already happened)
2) 1 * 1/4 = 1/4
3) 1 * 3/4 * 1/3 = 1/4
4) 1 * 3/4 * 2/3 * 1/2 = 1/4
5) 1 * 3/4 * 2/3 * 1/2 = 1/4

Giving you even money on getting blown away and not.

The problem here is, I can't remember how to figure out your chances of getting blown away if you just spin between every shot, but I'm pretty sure the person who shoots first is at a disadvantage. If that's true, you should take the even money proposition in Ed's example.

However, if you can spin the gun whenever you want, you should spin everytime after you shoot, and never after he does.

In short:

If you can spin whenever you want, optimal strategy is to let him shoot, then you shoot, then to re-spin.

If you have to decide before he shoots whether to always spin or never spin, you should choose to never spin.

And to answer Ed Miller's exact question: You shouldn't spin. (I assumed it's worse than even money for the first shooter to go back and forth spinning then shooting).
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