And the answer is . . .

The correct answer is that the ball costs 5 cents. Since the bat costs $1 more than the ball, the bat costs $1.05. The two together are then $1.05 + $0.05 = $1.10 as stated in the problem. Don't feel too badly, however, if you answered 10 cents. Almost everyone reports an initial tendency to answer “10 cents” because the sum $1.10 separates naturally into $1 and 10 cents, and 10 cents is about the right magnitude.

See Maps of Bounded Rationality: A Perspective on Intuitive Judgment and Choice, Nobel Prize Lecture, December 8, 2002 by Daniel Kahneman for an in-depth discussion of decision heuristics.

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