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
References