由 --- 於 星期二 四月 15, 2003 8:47 pm
Consider the princlple of inclusion and exclusion.
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X=P(某甲有A)=1-C(48,13)/C(52,13)=1-0.303817527=0.696182473
Y=P(某甲沒A)=C(48,13)/C(52,13)=0.303817527
YY=P(某甲沒A,2)=C(44,13)/C(52,13)=0.081754989
XY=P(某甲有A,沒2)=Y-YY=0.222062538
XX=P(某甲有A,2)=X-XY=0.474119935
...
XXXXX=P(某甲有A,2,3,4,5)=0.126614498
...
YXXXXX=P(某甲沒A,有2,3,4,5)=0.050824703
...
YXXXXXXXXXX=P(某甲沒6,有A,2,3,4,5,7,8,9,10,J)=0.00315144
YYXXXXXXXXXX=P(某甲沒3有45678,沒9有10JQKA)=0.001785844
P(某甲順子)
=P(某甲有A2345)
+P(某甲沒A有23456)
+P(某甲沒2有34567)
+P(某甲沒3有45678)
+P(某甲沒4有56789)
+P(某甲沒5有678910)
+P(某甲沒6有78910J)
+P(某甲沒7有8910JQ)
+P(某甲沒8有910JQK)
+P(某甲沒9有10JQKA)
-P(某甲有A2345,沒6有78910J)
-P(某甲有A2345,沒7有8910JQ)
-P(某甲有A2345,沒8有910JQK)
-P(某甲有A2345,沒9有10JQKA)
-P(某甲沒A有23456,沒7有8910JQ)
-P(某甲沒A有23456,沒8有910JQK)
-P(某甲沒A有23456,沒9有10JQKA)
-P(某甲沒2有34567,沒8有910JQK)
-P(某甲沒2有34567,沒9有10JQKA)
-P(某甲沒3有45678,沒9有10JQKA)
= XXXXX+YXXXXX*9-XXXXXXXXXXY*4-YYXXXXXXXXXX*6
=0.126614498+0.050824703*9-0.00315144*4-0.001785844*6
=0.560716001
p.s. P(4人都沒順子)~ P(某甲沒順子)^4~ (1-0.560716001)^4=0.037237588
SO, P(4人中至少有1人有順子)=1- P(4人都沒順子) ~ 0.962762412
this is 估計值
和 精確值 相差不遠!
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P(某甲沒pair)=P(某甲拿A2345678910JQK)
=4^13*C(13,13)/C(52,13)
=0.000105681
P(某甲有pair)=1-0.000105681=0.999894319
P(某甲拿同花順)
精確值
=0.016763393
=1/59.65379477
大概玩60次,某甲會碰到一次同花順 [/hide:161cd772f2]