Maths Olympiad Prep

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, 2005

Combinatorics Difficulty 1.0 Junior Find the answer Canada

A game is said to be fair if your chance of winning is equal to your chance of losing. How many of the following games, involving tossing a regular six-sided die, are fair?
• You win if you roll a 22
• You win if you roll an even number
• You win if you roll a number less than 44
• You win if you roll a number divisible by 33

(A) 00 (B) 11 (C) 22 (D) 33 (E) 44

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.