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Geek 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.

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

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

Solution :

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

There are 6 ways to arrange the revolver with consecutive bullets. These are the possible scenarios:

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

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

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

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

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

But if he re-spins, there are 2 bullets remaining and 6 total slots i.e. 2/6 or 33%.

So, she should prefer pulling the trigger again right away.