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Two Balls, No Strikes!

Imagine an urn with two balls, each of which may be either white or black.  One of these balls is drawn and is put back before a new one is drawn. Suppose that in the first two draws white balls have been drawn.  What is the probability of drawing a white ball on the third draw?

Essai philosophique sur les probabilités, Pierre-Simon Laplace, 1814

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"Two Balls, No Strikes!," Convergence (April 2004)