深林人不知
春芽
共回答了20个问题采纳率:85% 举报
(1)
![](https://img.yulucn.com/upload/a/e7/ae7389352598589108cbd2eb685db7bf_thumb.jpg)
.(2)
![](https://img.yulucn.com/upload/b/8e/b8e2a4e4aee249729b056cfc6b3f8759_thumb.jpg)
.
试题分析:古典概型概率的计算问题,需要计算基本事件空间总数及事件发生所包含的基本事件数,常用方法有“树图法”、“坐标法”,本题可以利用两种方法予以解答.
试题解析:解法一:利用树状图可以列出从甲、乙两个盒子中各取出1个球的所有可能结果:
可以看出,试验的所有可能结果数为16种.4分
(1)所取两个小球上的标号为相邻整数的结果有1-2,2-1,2-3,3-2,3-4,
4-3,共6种. 6分
故所求概率
![](https://img.yulucn.com/upload/a/e7/ae7389352598589108cbd2eb685db7bf_thumb.jpg)
.
答:取出的两个小球上的标号为相邻整数的概率为
![](https://img.yulucn.com/upload/6/c6/6c6b8eed2537644267d9136e088cb935_thumb.jpg)
. 8分
(2)所取两个球上的数字和能被3整除的结果有1-2,2-1,2-4,3-3,4-2,共5种.10分
故所求概率为
![](https://img.yulucn.com/upload/b/8e/b8e2a4e4aee249729b056cfc6b3f8759_thumb.jpg)
.
答:取出的两个小球上的标号之和能被3整除的概率为
![](https://img.yulucn.com/upload/f/32/f3287ecc4283fcfe70bd2160fafc87cf_thumb.jpg)
.12分
解法二:设从甲、乙两个盒子中各取1个球,其数字分别为
![](https://img.yulucn.com/upload/e/16/e1688eca88e06023504b12ce326fd15e_thumb.jpg)
,用
![](https://img.yulucn.com/upload/9/bc/9bc5cdbf48c3ccb5591c749553c6dfc8_thumb.jpg)
表示抽取结果,则所有可能有
![](https://img.yulucn.com/upload/8/4d/84d8c992ea307c676ad2725736979c72_thumb.jpg)
,
![](https://img.yulucn.com/upload/f/8e/f8ecd11484b9f74a40c2cb3fdf7b7da0_thumb.jpg)
,
![](https://img.yulucn.com/upload/7/12/712a9fddf1837bbf318d6a878ea00eb1_thumb.jpg)
,
![](https://img.yulucn.com/upload/5/15/5153907f6134c0b6c270854f77cecfb0_thumb.jpg)
,
![](https://img.yulucn.com/upload/2/f2/2f2b9db8880a297ef399bbebe3fccf32_thumb.jpg)
,
![](https://img.yulucn.com/upload/8/21/821199d9796d4bc1d1032db2d83e651e_thumb.jpg)
,
![](https://img.yulucn.com/upload/0/54/054319dd8a90ff4d1978a8392b4bb71a_thumb.jpg)
,
![](https://img.yulucn.com/upload/b/59/b59c24ff7ee546861a5adae0003167ec_thumb.jpg)
,
![](https://img.yulucn.com/upload/4/2f/42fa356aa85750f06de2fb24a522c788_thumb.jpg)
,
![](https://img.yulucn.com/upload/d/bd/dbd9659a527da481c56ce40060c11105_thumb.jpg)
,
![](https://img.yulucn.com/upload/8/da/8dabefe392fc3d6f9693d814c0beadcf_thumb.jpg)
,
![](https://img.yulucn.com/upload/a/83/a8343e9420adbfee2417c381ed6ea1ad_thumb.jpg)
,
![](https://img.yulucn.com/upload/0/56/056365455b35f3fefc6b6d9378a7cef9_thumb.jpg)
,
![](https://img.yulucn.com/upload/6/1e/61ea246afffabee5f7e4e946bc8672e0_thumb.jpg)
,
![](https://img.yulucn.com/upload/3/84/3844fa31d7e1e534c4aceb52c6c8d489_thumb.jpg)
,
![](https://img.yulucn.com/upload/e/2d/e2de12c11c69bb8652d4598ab244fb99_thumb.jpg)
,共16种. 4分
(1)所取两个小球上的数字为相邻整数的结果有
![](https://img.yulucn.com/upload/f/8e/f8ecd11484b9f74a40c2cb3fdf7b7da0_thumb.jpg)
,
![](https://img.yulucn.com/upload/2/f2/2f2b9db8880a297ef399bbebe3fccf32_thumb.jpg)
,
![](https://img.yulucn.com/upload/0/54/054319dd8a90ff4d1978a8392b4bb71a_thumb.jpg)
,
![](https://img.yulucn.com/upload/d/bd/dbd9659a527da481c56ce40060c11105_thumb.jpg)
,
![](https://img.yulucn.com/upload/a/83/a8343e9420adbfee2417c381ed6ea1ad_thumb.jpg)
,
![](https://img.yulucn.com/upload/3/84/3844fa31d7e1e534c4aceb52c6c8d489_thumb.jpg)
,共6种.6分
故所求概率
![](https://img.yulucn.com/upload/a/e7/ae7389352598589108cbd2eb685db7bf_thumb.jpg)
.
答:取出的两个小球上的标号为相邻整数的概率为
![](https://img.yulucn.com/upload/6/c6/6c6b8eed2537644267d9136e088cb935_thumb.jpg)
. 8分
(2)所取两个球上的数字和能被3整除的结果有
![](https://img.yulucn.com/upload/f/8e/f8ecd11484b9f74a40c2cb3fdf7b7da0_thumb.jpg)
,
![](https://img.yulucn.com/upload/2/f2/2f2b9db8880a297ef399bbebe3fccf32_thumb.jpg)
,
![](https://img.yulucn.com/upload/b/59/b59c24ff7ee546861a5adae0003167ec_thumb.jpg)
,
![](https://img.yulucn.com/upload/8/da/8dabefe392fc3d6f9693d814c0beadcf_thumb.jpg)
,
![](https://img.yulucn.com/upload/6/1e/61ea246afffabee5f7e4e946bc8672e0_thumb.jpg)
,共5种. 
1年前
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