HMMT 二月 2017 · 冲刺赛 · 第 8 题
HMMT February 2017 — Guts Round — Problem 8
题目详情
英文原题
- [ 6 ] You have 128 teams in a single elimination tournament. The Engineers and the Crimson are two ofthese teams. Each of the 128 teams in the tournament is equally strong, so during each match, eachteam has an equal probability of winning.
Now, the 128 teams are randomly put into the bracket.
What is the probability that the Engineers play the Crimson sometime during the tournament?
February 2017, February 18, 2017 — GUTS ROUND
Organization Team Team ID# 8
解析
英文解析
- [ 6 ] You have 128 teams in a single elimination tournament. The Engineers and the Crimson are two ofthese teams. Each of the 128 teams in the tournament is equally strong, so during each match, eachteam has an equal probability of winning.
Now, the 128 teams are randomly put into the bracket.
What is the probability that the Engineers play the Crimson sometime during the tournament?
Proposed by: Yang Liu
Answer:1
( )64
There are = 127 · 64 pairs of teams. In each tournament, 127 of these pairs play.128
127 12
By symmetry, the answer is = .
127 · 64 64 8