解题方法
1 . 某公司研发了两种具有自主知识产权的操作系统,分别命名为“天下”、“东方”.这两套操作系统均适用于手机、电脑、车联网、物联网等,且较国际同类操作系统更加流畅.
(1)为了解喜欢“天下”系统是否与性别有关,随机调查了
名男用户和
名女用户,每位用户对“天下”系统给出喜欢或不喜欢的评价,得到下面列联表:
![](https://img.xkw.com/dksih/QBM/2020/3/4/2412211081658368/2412598170247168/STEM/319e80f1b2204cedbb9e0ada3b5dac60.png?resizew=424)
请问:能否有
的把握认为男、女用户对“天下”系统的喜欢有差异?
附:
.
![](https://img.xkw.com/dksih/QBM/2020/3/4/2412211081658368/2412598170247168/STEM/8a22450dfab542e7810adc5e4109f1f5.png?resizew=281)
(2)该公司选定
万名用户对“天下”和“东方”操作系统(以下简称“天下”、“东方”)进行测试,每个用户只能从“天下”或“东方”中选择一个使用,每经过一个月后就给用户一次重新选择“天下”或“东方”的机会.这个月选择“天下”的用户在下个月选择“天下”的概率均为
,选择“东方”的概率均为
,
;这个月选择“东方”的用户在下个月选择“天下”的概率均为
,选择“东方”的概率均为
,
.记
表示第
个月用户选择“天下”的概率,已知
,
,
,
,
.
(ⅰ)求
的值;
(ⅱ)证明:数列
(
)为等比数列;
(ⅲ)预测选择“天下”操作系统的用户数量不超过多少万人.(精确到1万)
(1)为了解喜欢“天下”系统是否与性别有关,随机调查了
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6f1af4b44b2e97e8f319bab4ae9010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6f1af4b44b2e97e8f319bab4ae9010.png)
![](https://img.xkw.com/dksih/QBM/2020/3/4/2412211081658368/2412598170247168/STEM/319e80f1b2204cedbb9e0ada3b5dac60.png?resizew=424)
请问:能否有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d1052179ac2e82efd6fe0165423e1d.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://img.xkw.com/dksih/QBM/2020/3/4/2412211081658368/2412598170247168/STEM/8a22450dfab542e7810adc5e4109f1f5.png?resizew=281)
(2)该公司选定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadc63e6e33743ce590ed968948a5a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fc97b0acc21bf52197d5a1e793671a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1cd0cf755cb75c35aff6dc911b52f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5544d98eaae4004ed8735f09623d05a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b5c17dbc592004896ef47a48d9683b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0658483b45f620d0528761f36bb8cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8be264818fc810dff0bac75d49000be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0951ceb19806f12c1459e4b206c305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fb953225fe3b7470ca9914295a5268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
(ⅱ)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2c58faa560d1a8a0ac1f72e25ce09e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
(ⅲ)预测选择“天下”操作系统的用户数量不超过多少万人.(精确到1万)
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