MathDB
Turkey NMO 2000 1st Round - P15 (Combinatorics)

Source:

July 25, 2012
probability

Problem Statement

A,B,CA,B,C are playing backgammon tournament. At first, AA plays with BB. Then the winner plays with CC. As the tournament goes on, the last winner plays with the player who did not play in the previous game. When a player wins two successive games, he will win the tournament. If each player has equal chance to win a game, what is the probability that CC wins the tournament?
<spanclass=latexbold>(A)</span> 27<spanclass=latexbold>(B)</span> 13<spanclass=latexbold>(C)</span> 314<spanclass=latexbold>(D)</span> 17<spanclass=latexbold>(E)</span> None <span class='latex-bold'>(A)</span>\ \frac27 \qquad<span class='latex-bold'>(B)</span>\ \frac13 \qquad<span class='latex-bold'>(C)</span>\ \frac3{14} \qquad<span class='latex-bold'>(D)</span>\ \frac 17 \qquad<span class='latex-bold'>(E)</span>\ \text{None}