随机数法

(2) 已知随机函数Rand()产生的随机数的范围为x0x1, b,c是算法语句

b4Rand()和c4Rand()的执行结果．(注: 符号“”表示“乘号”)

【说明】本题主要考查随机数、随机函数的定义，古典概型，几何概型，线性规划等基

础知识，考查学生转换问题的能力，数据处理能力． 解：由f(x)x2bxc知，事件A “f(1)5且f(0)3”，即bc4····· 1分 . ·

c3 (1) 因为随机数b,c{1,2,3,4}，所以共等可能地产生16个数对(b,c)，

列举如下：

(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4)， (4,1),(4,2),(4,3),(4,4). ················································································ 4分

bc4事件A ：包含了其中6个数对(b,c)，即：

c3(1,1),(1,2),(1,3),(2,1),(2,2),(3,1). ································································· 6分

所以P(A)633，即事件A发生的概率为. ··········································· 7分 1688(2) 由题意，b,c均是区间[0,4]中的随机数，产生的点(b,c)均匀地分布在边长为4的正方形区域中（如图），其面积S()16. ······························ 8分

事件A ：bc4所对应的区域为如图所示的梯形（阴影部分），

c3115(14)3. ·························································· 10分 22c43(1,3)其面积为：S(A)

15S(A)215所以P(A)， S()1632

即事件A的发生概率为

O4b15. ·········································································· 12分 32