棋手的概率问题

最新推荐文章于 2026-01-06 22:02:48 发布

转载最新推荐文章于 2026-01-06 22:02:48 发布 · 249 阅读

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这是 PUZZLEUP 2014 的15题，ITPUB的oracle开发版有一专门的帖子
There are 24 players in a chess tournament. 8 teams participated with 2 players , and 8 teams participated with 1 player. For the 12 matches in the first round, the pairings will be drawn randomly. What is the probability that at least 4 matches will be played between players from the same school?

Enter your answer as a simplified fraction. Example:12/23

棋手

共有24名选手参加国际象棋比赛。 8支队有2名选手参加，8支队以1名选手参加。在第一轮的12场比赛，选手之间是随机配对的。
至少有四场比赛是在同一个学校的选手之间进行，这样的概率是多少？

将你的答案输入为简化分数，例如：12/23
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自我感觉概率统计学的还行，结果弄了半天还是没有推出公式，最后，写了个穷举法sql来算

--24个人
with a as (select power(2, rownum-1) rn, rownum rnc from dual connect by rownum <=24)
, b as (select rownum rn, a.rn+b.rn txx ,
--flag为1是同一队
case when b.rnc=a.rnc+1 and b.rnc<=16 and mod(b.rnc,2)=0 then 1 else 0 end flag
from a, a b where b.rn>a.rn)
,d (idx, rn, txx,flag) as
( select 1 idx, b.rn, b.txx , b.flag from b
union all
select d.idx+1, b.rn , d.txx +b.txx txx ,d.flag+b.flag
from d,b where b.rn>d.rn and bitand(d.txx,b.txx)=0
)
--4代表至少4队
select sum(case when d.flag>=4 then 1 else 0 end) ff, count(1) alll
,sum(case when d.flag>=1 then 1 else 0 end) / count(1)
--12是配成12队的
from d where d.idx=12