A Russian gangster kidnaps you. He puts two bullets in consecutive order in an empty six-round revolver, spins it, points it at your head and shoots.
*Click* You’re still alive!
He then asks you, “Do you want me to spin it again and fire or pull the trigger again right away?” Which option will give you a higher probability of not being shot at?
The option to pull the trigger again will give a higher probability of not being shot.
The key hint here is that the bullets were loaded adjacent to each other.
There are 4 ways to arrange the revolver with consecutive bullets so that the first shot is blank. These are the possible scenarios:
(xBBxxx)
(xxBBxx)
(xxxBBx)
(xxxxBB)
The other two scenarios would have meant you got shot on the first attempt. (BBxxxx) or (BxxxxB).
Now look at the second slot in the 4 possible scenarios above. The odds of getting shot are 1⁄4 or 25% (Only the first scenario would get you shot).
But if you respin, there are 2 bullets remaining and a total of 6 slots, which gives a probability of 2⁄6 or 33% of being shot.