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Odds favoring Team A

Source: 1971 AHSME Problem 23

April 22, 2014
probabilityAMC

Problem Statement

Teams A\text{A} and B\text{B} are playing a series of games. If the odds for either to win any game are even and Team A\text{A} must win two or Team B\text{B} three games to win the series, then the odds favoring Team A\text{A} to win the series are
<spanclass=′latex−bold′>(A)</span>11 to 5<spanclass=′latex−bold′>(B)</span>5 to 2<spanclass=′latex−bold′>(C)</span>8 to 3<spanclass=′latex−bold′>(D)</span>3 to 2<spanclass=′latex−bold′>(E)</span>13 to 6<span class='latex-bold'>(A) </span>11\text{ to }5\qquad<span class='latex-bold'>(B) </span>5\text{ to }2\qquad<span class='latex-bold'>(C) </span>8\text{ to }3\qquad<span class='latex-bold'>(D) </span>3\text{ to }2\qquad <span class='latex-bold'>(E) </span>13\text{ to }6
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