Originally posted by Syterion
Since Pontiuth has logged off, I'll ask the next question since I believe the present one is faulty and/or ridiculously easy. This one I will post is not too difficult, but I will require explanation.
There are three men, named John, Joe, and Jim. They have a dispute and obviously they decide to have a shootout. They draw straws to find the order of the shooting. They will take turns and the last man standing...wins, I guess. When one of them has a choice of who to shoot, he always chooses randomly.
You see, John and Joe both are perfect shots. All the time. 100%. Jim, unfortunately, only hits the mark half the time.
So, who has the best chance to survive the shootout?
Joe and John have equal chances. I worked it out below (took a while). Below is each possibility of the straw-drawings listed, and below each of these possibilities is the list of sub-possibilities, and below each of these is the chances for that particular straw-drawing.:
Edit: DAMN YOU, all that work for nothing!
John, Joe, Jim
50%: John shoots Joe, 50%: John shoots Jim. If John shoots Joe, then Jim tries to shoot John and 50% succeeds (and survives), 50% fails (and dies by being shot by John). If John shoots Jim, Joe shoots John and Joe survives.
CHANCES: John: 25%, Joe: 50%, Jim: 25%
John, Jim, Joe
50%: John shoots Jim, 50%: John shoots Joe. If John shoots Jim, Joe then shoots John and Joe survives. If John shoots Joe, Jim then shoots John and 50% succeeds (and survives) and 50% fails (and dies from being shot by John).
CHANCES: John: 25%, Joe: 50%, Jim: 25%
Joe, John, Jim
Same as first one, but alternate John/Joe.
Joe, Jim, John
Same as second one, but alternate John/Joe.
Jim, John, Joe
50% Jim tries to shoot John, 50% Jim tries to shoot Joe. If Jim tries to shoot John, 50% succeeds and 50% fails. If Jim tries to shoot Joe, 50% succeeds and 50% fails. If Jim shoots John, Joe shoots Jim and survives. If Jim shoots Joe, John shoots Jim and survives. If Jim fails to shoot anyone, 50% John shoots Jim and 50% John shoots Joe. If John shoots Jim, Joe shoots John and survives. If John shoots Joe, Jim shoots John and 50% succeeds (and survives) and 50% fails (and dies from being shot by John).
CHANCES: John: 37.5%, Joe: 50%, Jim: 12.5%
Jim, Joe, John
Same as above, but alternate John/Joe.