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If you get this right without having seen it before, that will be very impressive!
Three gentlemen, Col. Mustard, Mr. Green, and Prof. Plum, have offended each others' honor. They will settle their dispute with a duel with pistols.
They are not equally good shots.
| Prof. Plum | hits his target 1/3 of the time he shoots. |
| Mr. Green | hits his target 2/3 of the time he shoots. |
| Col. Mustard | hits his target every time he shoots. |
The three decide that they will take turns shooting. Prof. Plum will shoot first. Then Mr. Green will shoot, if Prof. Plum didn't shoot him. Then Col. Mustard will shoot, if he hasn't been shot yet. Then Prof. Plum, Mr. Green, and Col. Mustard again, if they haven't been shot yet. They keep taking turns until only one of them is unscathed. That one is the winner!
Prof. Plum has the first shot. Where should he aim, to maximize the probability that he will win?