试题分析:(Ⅰ)P真
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716640256.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716656852.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716656519.png)
;
Q真
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240027166711506.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716703558.png)
;
“P且Q”真
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716703583.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716718864.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716734523.png)
.
区间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716749503.png)
的长度为8,区间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716765495.png)
的长度为3,
故在区间(-4,4)上任取一个实数x,命题“P且Q”为真的概率
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716593524.png)
. …………6分
(Ⅱ)在(Ⅰ)的基础上易知,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716796528.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716796546.png)
,则基本事件
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716812537.png)
共有12个:(-2,-1),(-2,0),(-2,1),(-2,2),(-1,-1),(-1,0),(-1,1),(-1,2),(0, -1),(0,0),(0,1),(0,2).
“P或Q”真
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716640256.png)
P真或Q真
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716843517.png)
,符合
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716859954.png)
的基本事件为:(-2,-1),(-2,0),(-1,-1),(-1,0),(-11),(0, -1),(0,0),(0,1),(0,2),共9个.
故事件“
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716578968.png)
”发生的概率
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824002716625742.png)
. …………………………12分
点评:综合题,判断命题的真假,往往涉及知识方法较多,对复合命题,真值表的利用是常考点。古典概型概率的计算,公式明确,关键是计算基本事件数要准确,可借助于“树图法”“坐标法”。