MathDB
Nice Symmetry

Source: 2021 Fall AMC10 B P20

November 17, 2021
AMCAMC 10AMC 10 Bsymmetry

Problem Statement

In a particular game, each of 44 players rolls a standard 66{ }-sided die. The winner is the player who rolls the highest number. If there is a tie for the highest roll, those involved in the tie will roll again and this process will continue until one player wins. Hugo is one of the players in this game. What is the probability that Hugo's first roll was a 5,5, given that he won the game?
(<spanclass=latexbold>A</span>)61216(<spanclass=latexbold>B</span>)3671296(<spanclass=latexbold>C</span>)41144(<spanclass=latexbold>D</span>)185648(<spanclass=latexbold>E</span>)1136(<span class='latex-bold'>A</span>)\: \frac{61}{216}\qquad(<span class='latex-bold'>B</span>) \: \frac{367}{1296}\qquad(<span class='latex-bold'>C</span>) \: \frac{41}{144}\qquad(<span class='latex-bold'>D</span>) \: \frac{185}{648}\qquad(<span class='latex-bold'>E</span>) \: \frac{11}{36}