Puzzle Details :

a lady got kidnapped by a gangster. The Gangster puts two bullets in consecutive order in an empty six-round revolver, spins it, points it at her head, and shoots. She is still alive. The Gangster then asked her,

“Do you want me to spin it again and fire or pull the trigger again right away?”

Which option should be preferred? For each option, what is the probability that she’ll be shot?

The most important point here to consider is that the bullets were loaded adjacent to each other.

There are 6 ways to arrange the 6-round revolver with consecutive bullets. These are the possible scenarios that can be arranged with the 2 consecutive bullets:

(xBBxxx)
(xxBBxx)
(xxxBBx)
(xxxxBB)
(BBxxxx)
(BxxxxB)

But, the first shot went blank and hence the last two possibilities are of no use.

we can easily eliminate these possibilities. Let me explain this in detail.

as per the question, the gangster was already shot once, and it is blank. This implies that in the combinations first value cannot be B it must be x which is empty. hence the combination starting with B must be eliminated.

So, now the 4 possible arrangements of the consecutive bullets, considering the first blank attempt are these:

(xBBxxx)
(xxBBxx)
(xxxBBx)
(xxxxBB)

Now, looking at these possibilities, her odds of getting shot are 1/4 or 25%. (case: xBBxxx).

This is the only combination she will get shot with, in all other combinations the immediate one is blank.

But if he re-spins, then the following are the combinations

(xBBxxx)
(xxBBxx)
(xxxBBx)
(xxxxBB)
(BBxxxx)
(BxxxxB)

as we can see here, there are 2 possibilities out of 6 combinations where a lady will be shot.

looking at these possibilities, her odds of getting shot here is 2/6 or 33%.

So, she should prefer pulling the trigger again right away which is a 25% possibility of getting shot instead of re-spin which increases to 33% of getting shot. This is the solution to this puzzle.