If the second shot goes empty, you will be spared by him. What will you choose?

Question

Welcome to the deadly game placed by the serial killer Jigsaw. You are tied to a chair and you cant move your hands or get up. Jigsaw shows you an empty gun with all the six chambers empty. He puts two bullets in the adjacent chambers and then close the barrel. He spins it and then point the gun to your head. The first shot snaps. It was an empty slot.

Now before pressing the trigger again, he asks you whether to pull the trigger or to spin the barrel first and then pull the trigger.

If the second shot goes empty, you will be spared by him. What will you choose?

Also think what will you chose if the bullets are not in the adjacent chambers.

Answer 1

Don't spin.
Let's call the filled chambers, chambers 1 and 2.
As the first shot was empty, that was chamber 3, 4, 5 or 6. Only in the case of chamber 6 will you die => 75% you live (3 in 4 options).
If the spin is random there is no bullet in 4 of the 6 chambers = 67% you live (4 in 6 options).

If the bullets are not adjacent you should spin (no spin is 60% you live vs 67% you live with spin).

Answer 2

Answer: Here, you have better chances of survival if you chose to spin the barrel.
1) If bullets are placed in the adjacent chambers:
Let us do this step by step. The possible combinations for the bullets are:
1, 2
2, 3
3, 4
4, 5
5, 6
6, 1
Now if you ask not to spin the barrel:
The first shot went empty and thus the events (6, 1) and (1, 2) dont have bullets in them. Now only four possible shots are available.
Thus, P (death) = 1/4 = 0.25
P (Survival) = 1- 0.25 = 0.75
If you ask to spin the barrel:
Since you were not hit in the first shot, therefore
P (death) in the second shot = 2/6 = 0.33
P (Survival) in the second shot = 1 - 0.33 = 0.77
Clearly, you will have better chances of survival if you ask him not to spin the barrel.
2) If bullets are not placed in the adjacent slots:
If you dont spin it:
You were not hit in the first shot. Thus,
P (Death) in second shot = 2/5 = 0.4
P (Survival) in second shot = 1 - 0.4= 0.6
If you spin the barrel
P (death) in the second shot = 2/6 = 1/3 = 0.33
P (Survival) in second shot = 1 - 0.33 = 0.77
Here, you have better chances of survival if you chose to spin the barrel.