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....
What happens if the two bullets aren't adjacent to each other in the barrel....
Possible combinations of both bullets
1,2
2,3
3,4
4,5
5,6
6,1
Don't Spin case
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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-
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P(death)=2/6=1/3 = .33
p(survival) = .77
So don't spin it.
2nd case:
Don't Spin It case
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Not hit in the first case so
P(death) in second hit = 2/5 = .4
Spin it case
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P(death) in second hit = 2/6 = .3
So he should spin it if bullets aren't adjacent