John is lying on the sidewalk after robbing a bank, in pain andmulling over how to quantify the uncertainty of his survival, whenDirty Harry walks over. Dirty Harry pulls out his 44 Magnum andputs two bullets opposite each other in the six slots in thecylinder (e.g., if you number them 1 .. 6 clockwise, he puts themin 1 and 4), spins the cylinder randomly, and, saying "The questionis, are you feeling lucky, probabalistically speaking, computerscience punk?" points it at John head and pulls the trigger...."CLICK!" goes the gun (no bullet) and Dirty Harry smiles... "Howabout that .... Let's see if this gun is memory-less!" Withoutspinning the cylinder again, he points the gun at Wayne's head andpulls the trigger again.
(a) What is the probability that (at least in my dream) John ishit?
(b) Now, suppose that when Dirty Harry put the bullets in thegun, he put them right next to each other (e.g., in slots 1 and 2).He spins it as usual. What is the probability in this case John ishit?
(c) Suppose Dirty Harry puts the bullets in two random positionsin the cylinder and we don't have any idea where they are. He spinsit as usual. Now what is the probability that John will be hit?
