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1 . 如图,某市有南、北两条城市主干道,在出行高峰期,北干道有
,
,
,
,四个交通易堵塞路段,它们被堵塞的概率都是
,南干道有
,
,两个交通易堵塞路段,它们被堵塞的概率分别为
,
.某人在高峰期驾车从城西开往城东,假设以上各路段是否被堵塞互不影响.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/c5760ed0-442b-40d5-b0a0-f7dc404be399.png?resizew=354)
(1)求北干道的
,
,
,
个易堵塞路段至少有一个被堵塞的概率;
(2)若南干道被堵塞路段的个数为
,求
的分布列及数学期望
;
(3)若按照“平均被堵塞路段少的路线是较好的高峰期出行路线”的标准,则从城西开往城东较好的高峰期出行路线是哪一条?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7688363f5ffff23a6193c7a8eee501c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5815cc29f60d2aa538c4dd30e0803a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d1bd9858f86566b43bf41413563416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e02479c70f1b8851ce4fbb264d24b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/c5760ed0-442b-40d5-b0a0-f7dc404be399.png?resizew=354)
(1)求北干道的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7688363f5ffff23a6193c7a8eee501c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5815cc29f60d2aa538c4dd30e0803a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d1bd9858f86566b43bf41413563416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e02479c70f1b8851ce4fbb264d24b98.png)
(2)若南干道被堵塞路段的个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
(3)若按照“平均被堵塞路段少的路线是较好的高峰期出行路线”的标准,则从城西开往城东较好的高峰期出行路线是哪一条?请说明理由.
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2022-01-03更新
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