计算机问题求解-2013-03-26-离散概率基础.ppt

计算机问题求解–????? - ?????? 201 3年 03 月 26 日离散概率模型 A process : 掷两个色子 Sample space e Event probability Axioms for a probability space 满足下列性质的 P称为一个 probability distribution 或者一个 probability measure 。记住: P是一个函数。 Tree Diagrams: 结合计数与概率过程: 从下列硬币中依次取两枚: nickel: 1 dime: 2 quarter: 2 ??????????????????????????????有限样本空间? There are only finite es. ? Each es individually consists an elementary event. ? For one coin toss, there are two es – head and tail. “ Head ” is an elementary event. ? The probability of an elementary event corresponds a specific e. ? If all es are equally likely, then the probability of an event E can puted as: es of number total in es of number total || ||)( E A EEp??不满足 equally likely 分布的例子交集非空的事件?掷均匀的色子,掷 3次。出现事件“或者 3次均相等,或者没有一次是 4”的概率是多少? ?合理假设:每个 e 出现的可能性是一样的。?样本空间大小是 6 3 =216 。?用F表示事件“3次结果一样”,则|F |=6 (F ={111,222, …,666}) ?用G表示事件“没有一次结果是 4”,则|G |=5 3 =125 (G是从集合{1,2,3,5,6} 中任选 3个数的组合数) ?要求的事件为 F和G的并集: |F?G |=| F |+| G |-|F?G |=6+125-5=126 ?因此,最终结果是: 126/216 = 7/12 This is a special case of so-called inclusion- exclusion principle