Saturday, January 21, 2012

Russian roulette

Arnold has a revolver which holds up to six bullets. There are two bullets in the gun, in adjacent chambers. He decides to play Russian roulette (on his own!). He first spins the cylinder so that he does not know where the bullets are and then pulls the trigger.

Assuming that Arnold survives this first attempt, is he now better off pulling the trigger a second time without spinning the cylinder again or would he be better off spinning the cylinder again before pulling the trigger?

1 comment:

ErnestoDR said...

Here is my solution:
a) The probability of surviving during the first click is 4/6, since there are 4 empty chambers out of six (2 have the bullets). Assuming Arnold survives the first click, and he spins the cylinder again, his probability of surviving the second click is the same 4/6 or 0.67
b) However, if Arnold does not spin the cylinder, his chance of surviving the second click is 3/4 or 0.75, 3 empty chambers out of 4.
So he is better off not spinning the cylinder a second time.
Where the chamber stops after the first click of the gun is critical if the bullets are placed next to each other. No matter how high Arnold's survival probabilities are, I would not want to be in his situation!
Just a brain exercise!