You are trapped in one of the deathtraps laid by Jigsaw from the popular movie franchise Saw. In this trap, you are lying down in a bed strapped tightly with no choice other than listening to the video tape that is playing in front of you. A gun is raised and you see that the chambers are empty. A mechanical hand puts two bullets in the adjacent chambers of the barrel and then the barrel closes. The barrel is then spun.
The first shot is fired at you and it turns out to be empty. Now the video tape tells you that you have two options. You can either ask for the barrel to be spun again or ask for the second shot without spinning. If the second shot turns out to be empty, you will be spared.
What will you decide?
Also, for an alternative case, what will you do if the bullets are not placed in the adjacent chambers?
Solution:
First Case:
The possible combinations of the adjacent bullets placed in the chambers are:
1, 2
2, 3
3, 4
4, 5
5, 6
6, 1
Now if you don't spin the barrel:
The first shot was empty and thus the combinations of (6, 1) and (1, 2) surely don't have bullets. This means that the bullets are present in some other possible 4 slots.
Therefore P (Death) = 1/4 = 0.25
P (Survival) = 3/4 = 0.75
If you chose to spin the barrel:
P (Death) = 2/6 = 1/3 = 0.33
P (Survival) = 4/6 = 2/3 = 0.77
Therefore you must not ask to spin the barrel and you will have a better chance at surviving.
Second Case:
If you don't spin it:
You were not hit in the first shot. Thus,
P (Death) in second hit = 2/5 = 0.4
P (Survival) in second hit = 3/5 = 0.6
If you spin the barrel
P (death) in the second hit = 2/6 = 1/3 = 0.33
P (Survival) in second hit = 4/6 = 2/3 = 0.77
Thus in this case, you have better survival rate if you chose to spin the barrel.