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It's actually a 66.66666...% chance of the other box winning.
Why? Because the information changed. Essentially, you gave the participant a choice of choosing ONE box (which would be the choice if he stuck with the original box) or choosing TWO boxes, one of which can't win and that one would be revealed as a loser (at which point the participant would switch their choice from the original to the other one).
Run the stats, and switching will always reveal a greater chance of a win.
What would you pick... one box with a 33.3333...% chance of Winning, or TWO boxes, each with a combined chance of 66.66666...% chance of winning?
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