1)从52张扑克牌(去掉大小王)中随机取出12张牌,12张牌中有一张及以上A的概率:
1-C(52-4,12)/C(52,12)
=1-40*39*38*37/(52*51*50*49)
=1-38*37/(17*5*49)
=1-1406/4165
=2759/4165
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2)从52张扑克牌(去掉大小王)中随机取出4张牌之后,再随机取出12张牌,12张牌中有一张及以上A的概率:
1-C(40,4)/C(52,4)
=1-40*39*38*37/(52*51*50*49)
=1-38*37/(17*5*49)
=1-1406/4165
=2759/4165
总共有C(52,16) = y种;
有4种情况
1,前4张中若抽到1张A, 则C(4,1)C(48,3)(C(3,1)C(45,11)+C(3,2)C(45,10)+C(3,3)C(45,9)) = x1种;
2,前4张中若抽到2张A, 则C(4,2)C(48,2)(C(2,1)C(46,11)+C(2,2)C(46,10)) = x2种;
3,前4张中若抽到3张A, 则C(4,3)C(48,1)C(1,1)C(47,11) = x3种;
4,前4张中若抽到0张A, 则C(48,4)(C(4,1)C(44,11)+C(4,2)C(44,10)+C(4,3)C(44,9)+C(4,4)C(44,8)) = x4种;
概率为(x1+x2+x3+x4)/y;