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Problem 823

AMC 10/12, early questions

Combinatorics Difficulty 3.8 Multiple choice CEMC Gauss (Grade 8) · Canada · 2017

Mike and Alain play a game in which each player is equally likely to win. The first player to win three games becomes the champion, and no further games are played. If Mike has won the first game, what is the probability that Mike becomes the champion?

Pick one

Official solution

Given 8 dimes (10 coins) and 3 quarters (25 coins), we list the different amounts of money (in cents) that can be created in the table below.

When an amount of money already appears in the table, it has been stroked out.

FLAG: recreate complex table with strikethroughs, originally tikz drawing

We may ignore the first entry in the table, 0, since we are required to use at least one of the 11 coins.

We are left with 27 different amounts of money that can be created using one or more of the 8 dimes and 3 quarters.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.