鲁不格
幼苗
共回答了11个问题采纳率:100% 举报
容斥原理
A1∪A2∪A3∪..∪An=A1+A2+.+An-A1∩A2-A1∩A3-..-A1∩An-A2∩A3-..-A(n-1)∩An+A1∩A2∩A3+.+(-1)^(n+1)A1∩A2∩...∩An
每把钥匙插对概率为1/5
每两把钥匙插对概率为1/20
每3把钥匙插对概率为1/60
每四把钥匙插对概率为1/120
5把都插对概率为1/120
则至少有1把钥匙插对的概率为
C(5,1)*1/5-c(5,2)*1/20+C(5,3)*1/60-C(5,4)*1/120+C(5,5)*1/120
=1-1/2+1/6-1/24+1/120
=19/30
若有6把钥匙
每把钥匙插对概率1/6
每两把插对1/30
每三把1/120
每四把1/360
每五把1/720
6把1/720
至少1把插对概率为
C(6,1)*1/6-C(6,2)*1/30+C(6,3)*1/120-C(6,4)*1/360+C(6,5)*1/720-C(6,6)*1/720
=1-1/2+1/6-1/24+1/120-1/720
=91/144
1年前
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