simon2315
春芽
共回答了29个问题采纳率:93.1% 举报
(1)
![](https://img.yulucn.com/upload/0/4b/04b47afc90488fe9b37a9ec6443741f4_thumb.jpg)
;(2)当
![](https://img.yulucn.com/upload/e/d8/ed8d27dceec63ab6ec3ef8be437413e5_thumb.jpg)
,时
![](https://img.yulucn.com/upload/8/5f/85ff328c92e0cf16057c216e82c7f186_thumb.jpg)
,即先回答问题A,再回答问题B,获奖的期望值较大;当
![](https://img.yulucn.com/upload/f/4b/f4bdb604d1290cf4c56d388fa27c30d0_thumb.jpg)
,时
![](https://img.yulucn.com/upload/a/ac/aac4e9b6718e1732934d77c49d605eb6_thumb.jpg)
,两种顺序获奖的期望值相等;当
![](https://img.yulucn.com/upload/4/53/4530f46eef2af40c09e063b520defba9_thumb.jpg)
,时
![](https://img.yulucn.com/upload/d/c1/dc1b6ab9964e30d53aa6205e8b647f10_thumb.jpg)
,先回答问题B,再回答问题A,获奖的期望值较大.
试题分析:本题考查生活中的概率的计算公式和离散型随机变量的分布列和数学期望等基础知识,考查运用概率知识解决简单实际问题的能力,考查学生的分析能力和计算能力.第一问,参与者先回答问题
![](https://img.yulucn.com/upload/d/77/d77c14bd5c5e4bc03d8fa720785548f9_thumb.jpg)
,恰好获得奖金
![](https://img.yulucn.com/upload/8/f9/8f9c9a9c8357d81da4cc48016b70f982_thumb.jpg)
元,说明了问题
![](https://img.yulucn.com/upload/d/77/d77c14bd5c5e4bc03d8fa720785548f9_thumb.jpg)
答对了,而问题
![](https://img.yulucn.com/upload/a/89/a890f57ebd4c96718f16726d5ed39620_thumb.jpg)
没有答对,利用随机猜对问题
![](https://img.yulucn.com/upload/d/77/d77c14bd5c5e4bc03d8fa720785548f9_thumb.jpg)
的概率
![](https://img.yulucn.com/upload/f/ad/fad6fc17cc2440c3a75de583fb5e719c_thumb.jpg)
,随机猜对问题
![](https://img.yulucn.com/upload/a/89/a890f57ebd4c96718f16726d5ed39620_thumb.jpg)
的概率
![](https://img.yulucn.com/upload/9/c0/9c094ec25b4544cffe5c22b53a126638_thumb.jpg)
, 求所求概率;第二问,分别求出先回答问题
![](https://img.yulucn.com/upload/d/77/d77c14bd5c5e4bc03d8fa720785548f9_thumb.jpg)
再回答问题
![](https://img.yulucn.com/upload/a/89/a890f57ebd4c96718f16726d5ed39620_thumb.jpg)
, 先回答问题
![](https://img.yulucn.com/upload/a/89/a890f57ebd4c96718f16726d5ed39620_thumb.jpg)
再回答问题
![](https://img.yulucn.com/upload/d/77/d77c14bd5c5e4bc03d8fa720785548f9_thumb.jpg)
的概率和期望值,由于得到的期望值中含有字母,所以作差比较大小,分情况讨论2个期望值的大小.
试题解析:随机猜对问题
![](https://img.yulucn.com/upload/d/77/d77c14bd5c5e4bc03d8fa720785548f9_thumb.jpg)
的概率
![](https://img.yulucn.com/upload/f/ad/fad6fc17cc2440c3a75de583fb5e719c_thumb.jpg)
,随机猜对问题
![](https://img.yulucn.com/upload/a/89/a890f57ebd4c96718f16726d5ed39620_thumb.jpg)
的概率
![](https://img.yulucn.com/upload/9/c0/9c094ec25b4544cffe5c22b53a126638_thumb.jpg)
.2分
⑴设参与者先回答问题
![](https://img.yulucn.com/upload/d/77/d77c14bd5c5e4bc03d8fa720785548f9_thumb.jpg)
,且恰好获得奖金
![](https://img.yulucn.com/upload/8/f9/8f9c9a9c8357d81da4cc48016b70f982_thumb.jpg)
元为事件
![](https://img.yulucn.com/upload/f/92/f92f9b0629672b0fadaba931a74caff8_thumb.jpg)
,
则
![](https://img.yulucn.com/upload/5/36/53605cfef656664a4d6f490165382e3f_thumb.jpg)
,
即参与者先回答问题
![](https://img.yulucn.com/upload/d/77/d77c14bd5c5e4bc03d8fa720785548f9_thumb.jpg)
,其恰好获得奖金
![](https://img.yulucn.com/upload/8/f9/8f9c9a9c8357d81da4cc48016b70f982_thumb.jpg)
元的概率为
![](https://img.yulucn.com/upload/0/4b/04b47afc90488fe9b37a9ec6443741f4_thumb.jpg)
. 4分
⑵参与者回答问题的顺序有两种,分别讨论如下:
①先回答问题
![](https://img.yulucn.com/upload/d/77/d77c14bd5c5e4bc03d8fa720785548f9_thumb.jpg)
,再回答问题
![](https://img.yulucn.com/upload/a/89/a890f57ebd4c96718f16726d5ed39620_thumb.jpg)
.参与者获奖金额
![](https://img.yulucn.com/upload/4/4a/44a0908d8dc84bce2c28c01947beb860_thumb.jpg)
可取
![](https://img.yulucn.com/upload/1/52/15299a201dd42cffbd0bde2aafbf102e_thumb.jpg)
,
则
![](https://img.yulucn.com/upload/9/ad/9ad369e21dd746ced68a443d7362fedc_thumb.jpg)
,
![](https://img.yulucn.com/upload/a/d0/ad016fbe2214e70e7e357f3cdb0d6131_thumb.jpg)
,
②先回答问题
![](https://img.yulucn.com/upload/a/89/a890f57ebd4c96718f16726d5ed39620_thumb.jpg)
,再回答问题
1年前
4