Question

甲、乙隊(duì)各有3名柔道選手，代號(hào)分別為甲₁、甲₂、甲₃和乙₁、乙₂、乙₃，兩隊(duì)隊(duì)員之間甲隊(duì)隊(duì)員獲勝的概率如下表所示．

（1）若兩隊(duì)之間進(jìn)行對(duì)抗賽，一隊(duì)中至少有兩名選手戰(zhàn)勝對(duì)方才算是此隊(duì)獲勝，那么按甲₁對(duì)乙₂，甲₂對(duì)乙₁，甲₃對(duì)乙₃，甲隊(duì)獲勝的概率是多少？
（2）怎樣編排兩隊(duì)之間的對(duì)抗賽，甲隊(duì)獲勝的概率最大？最大概率為多少？

Answer 1

解：（1）若僅甲₁對(duì)乙₂，甲₂對(duì)乙₁獲勝，概率為0.6×0.5×0.2=0.06，
若僅甲₁對(duì)乙₂，甲₃對(duì)乙₃獲勝，概率為 0.6×0.5×0.8=0.24，
若僅甲₂對(duì)乙₁，甲₃對(duì)乙₃獲勝，概率為0.2×0.5×0.4=0.04，
若甲₁對(duì)乙₂，甲₂對(duì)乙₁，甲₃對(duì)乙₃都獲勝，概率為 0.6×0.2×0.5=0.06，
故甲隊(duì)獲勝的概率是0.06+0.24+0.04+0.06=0.4．
（2）由表格可知甲隊(duì)中水平是甲₁最高，甲₂其次，甲₃最低；
乙隊(duì)中水平是乙₁最高，乙₂其次，乙₃最低．
所以按甲₁對(duì)乙₂，甲₂對(duì)乙₃，甲₃對(duì)乙₁編排，甲隊(duì)獲勝的概率最大，
最大概率為P=0.6×0.6×0.1+0.6×0.6×0.9+0.6×0.4×0.1+0.4×0.6×0.1=0.408．