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Function: require_once

수학동아 - 폴리매스
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깊이 고민해볼 수 있는 수학 문제를 내는 곳입니다
[세상을 바꿀 문제] 균형잡힌 비이행성 주사위와 확률의 상한
△π 2021.02.18 02:26 조회 765
문제 푼 사람 0명
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

n개의 면을 가진 주사위가 3개 있다. 이 때, 어느 하나를 선택하더라도 이보다 높은 수가 나올 확률이 1/2보다 큰 주사위 세 개를 '비이행성 주사위'라고 한다. 또, 어느 하나가 다른 하나보다 높은 수가 나올 확률이 모두 동일한 주사위를 '균형잡힌 주사위'라고 하자.

 

(1)'n이 6 이상인 정수일 때, 균형잡힌 비이행성 주사위는 항상 존재한다'라는 명제를 증명하거나 반증하시오.

(2)균형잡힌 비이행성 주사위가 다른 주사위를 이길 확률의 상한을 구하여라.

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