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A box contains 7 black balls and a single red ball. Peter and Frances draw without replacement...

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Basic Math

Abox contains 7 black balls and a single red ball. Peter and Francesdraw without replacement balls from this urn, alternating aftereach draw until the red ball is drawn. The game is won by theplayer who happens to draw the single red ball. Peter is agentleman and offers Frances the choice of whether she wants tostart or not. Frances has a hunch that she might be better off ifshe starts; after all, she might succeed in the first draw. On theother hand, if her first draw yields a black ball, then Peter’schances to draw the red ball in his first draw are increased,because then one black ball is already removed from the urn. Howshould Frances decide in order to maximize her probability ofwinning?

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