Sunday, May 11, 2014

Russian Roulette

Problem

Lets play a game of Russian roulette. You are tied to a chair and can't get up. Here is the gun , six chambers all empty. Now I put two bullets in the gun and I put these bullets in the adjacent chambers. I close the barrel and spin it. I put the gun to your head and pull the trigger. Click and the slot was empty. Now before we start the interview I want to pull the trigger one more time , which one do you prefer , that I spun the barrel first or that I just pull the trigger ?

What happens if  the two bullets aren't adjacent to each other in the barrel.... 
 

Solution

1st Case:
Possible combinations of both bullets
1,2
2,3
3,4
4,5
5,6
6,1


Don't Spin case
---------------

Since you are not shot in the first one so (6,1)& (1,2) doesn't have the bullet's and they are in one of the other possible 4 slots

P(death)=1/4 = .25
p(survival)= .75

Spin it case-
-------------
P(death)=2/6=1/3 = .33
p(survival) = .77

So don't spin it.

2nd case:
Don't Spin It case
------------------
Not hit in the first case so
P(death) in second hit = 2/5 = .4

Spin it case
--------------
P(death) in second hit = 2/6 = .3

So he should spin it if bullets aren't adjacent

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