From 690b6b22f18eec30b793460175cf4afb42cc5c7d Mon Sep 17 00:00:00 2001
From: wangweiye7840 <kj_wangweiye@126.com>
Date: Thu, 6 Jul 2023 15:20:39 +0800
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---
 工具v2/批量收录题目.py |    2 +-
 题库0.3/Problems.json  | 1298 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 1299 insertions(+), 1 deletion(-)

diff --git a/工具v2/批量收录题目.py b/工具v2/批量收录题目.py
index 3e9a3ec2..e60b115c 100644
--- a/工具v2/批量收录题目.py
+++ b/工具v2/批量收录题目.py
@@ -1,5 +1,5 @@
 #修改起始id,出处,文件名
-starting_id = 18663 #起始id设置, 来自"寻找空闲题号"功能
+starting_id = 18725 #起始id设置, 来自"寻找空闲题号"功能
 raworigin = "" #题目来源的前缀(中缀在.tex文件中)
 filename = r"C:\Users\wangweiye\Documents\wwy sync\临时工作区\空中课堂必修第二册例题与习题.tex" #题目的来源.tex文件
 editor = "王伟叶" #编辑者姓名
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 441fa941..991a286a 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -481627,6 +481627,1304 @@
         "space": "4em",
         "unrelated": []
     },
+    "018725": {
+        "id": "018725",
+        "content": "判断下面哪些是随机现象, 哪些是确定性现象.\\\\\n(1) 如果$a>b$, 那么$a-b>0$;\\\\\n(2) 掷一枚硬币, 出现正面朝上;\\\\\n(3) 在数轴上任取一个点, 这个点所对应的数是有理数.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018726": {
+        "id": "018726",
+        "content": "分析下面两句话里含有怎样的随机性.\\\\\n(1) 行人闯红灯, 容易发生交通事故;\\\\\n(2) 有心栽花花不发, 无心插柳柳成荫.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018727": {
+        "id": "018727",
+        "content": "法国科学家蒲丰在$1777$年提出的著名的蒲丰投针实验. 这一实验的步骤是:\\\\\n\\textcircled{1} 取一张白纸, 在上面画上许多条间距为$a$的平行线.\\\\\n\\textcircled{2} 取一根长度为$l(l \\leq a)$的针, 随机地向画有平行直线的纸上投掷$m$次, 观察针与直线相交的次数$n$.\\\\\n\\textcircled{3} 计算$\\dfrac{2 l m}{a n}$的值.\\\\\n请同学们行动起来, 亲自做一次蒲丰投针实验, 完成以下任务:\\\\\n(1) 不妨令$m=1000$, 计算$\\dfrac{2 l m}{a n}$的值, 并验证$\\dfrac{2 l m}{a n}$的值是否接近于$\\pi$;\\\\\n(2) 查阅蒲丰投针实验的有关资料, 了解蒲丰投针实验的意义.\\\\\n建议$2$至$3$位同学组成项目小组, 以小组为单位完成上述任务. 进一步的建议如下:\\\\\n\\textcircled{1} 成立项目小组, 确定任务目标, 准备实验工具;\\\\\n\\textcircled{2} 分工合作, 明确责任. 例如, 测量、记录数据、计算求解、撰写报告等具体由谁负责;\\\\\n\\textcircled{3} 撰写报告, 讨论交流. 可以用照片、电脑幻灯片等形式展示获得的成果.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018728": {
+        "id": "018728",
+        "content": "写出下面随机试验的样本空间:\\\\\n(1) 抛掷一枚硬币, 观察朝上的面;\\\\\n(2) 掷一颗骰子(每一面上分别标注数字$1$、$2$、$3$、$4$、$5$、$6$的质地均匀的小正方体), 观察朝上的点数;\\\\\n(3) 从装有标号为$1$、$2$、$3$的三个球的袋子中依次取两个球(第一次取出的球不再放回), 观察标号, 考虑标号顺序;\\\\\n(4) 从装有标号为$1$、$2$、$3$的三个球的袋子中依次取两个球(第一次取出的球不再放回), 观察标号, 不考虑标号顺序;\\\\\n(5) 连续掷一颗骰子, 直到点数$6$出现为止, 观察掷的次数;\\\\\n(6) 向一面墙随机掷飞镖, 观察其在墙面上的落点.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018729": {
+        "id": "018729",
+        "content": "掷一颗骰子, 观察朝上的点数. 写出下列事件相应的样本空间的子集:\\\\\n(1) 点数$6$没有出现;\\\\\n(2) 出现偶数;\\\\\n(3) 点数不超过$2$.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018730": {
+        "id": "018730",
+        "content": "掷两颗骰子, 试表示其样本空间以及掷出的两个点数都是偶数这个事件所对应的子集.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018731": {
+        "id": "018731",
+        "content": "写出抛掷两枚硬币的样本空间.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018732": {
+        "id": "018732",
+        "content": "一只不透明的口袋内装有质地和大小完全相同的$3$个球, 且分别标有$1$、$2$、$3$三个号码, 从袋中不放回地依次抽取$2$个球, 观察两个球的号码.记``第一个球的号码是$1$''为事件$A$, ``第二个球的号码是$2$''为事件$B$, ``第一个球的号码是$1$且第二个球的号码是$2$''为事件$C$, ``第一个球的号码是$1$或者第二个球的号码是$2$''为事件$D$, ``第一个球的号码不是$1$''为事件$E$.\\\\\n(1) 分别写出样本空间$\\Omega$和事件$A$、$B$、$C$、$D$、$E$所对应的子集;\\\\\n(2) 分析事件$A$、$B$、$C$、$D$、$E$所对应的集合之间的关系.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018733": {
+        "id": "018733",
+        "content": "抛掷一枚硬币正面朝上和掷一颗骰子得点数$6$的概率分别是多少?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018734": {
+        "id": "018734",
+        "content": "掷一颗骰子, 观察掷出的点数, 求掷得奇数点的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018735": {
+        "id": "018735",
+        "content": "同时掷两颗骰子, 求:\\\\\n(1) 所得点数之和为$5$的概率;\\\\\n(2) 所得点数相等的概率;\\\\\n(3) 所得点数都是偶数的概率;\\\\\n(4) 所得点数相差$2$的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018736": {
+        "id": "018736",
+        "content": "判断下面的解答是否正确, 并说明理由.\\\\\n{\\it 某运动员连续进行两次飞碟射击练习, 观察命中目标的情况, 用$y$表示命中, 用$n$表示没有命中, 那么试验的样本空间$\\Omega=\\{y y, y n, n y, n n\\}$, 因此事件``两次射击都命中''的概率为$0.25$}.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018737": {
+        "id": "018737",
+        "content": "从$20$位同学中随机抽取一位, 已知抽到男生的概率为$0.3$, 求这$20$位同学中男生的人数.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018738": {
+        "id": "018738",
+        "content": "从$0 \\sim 9$这$10$个数中随机选择一个数, 求下列事件的概率:\\\\\n(1) 这个数的平方的个位数字为$1$;\\\\\n(2) 这个数的四次方的个位数字为$1$.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018739": {
+        "id": "018739",
+        "content": "掷两个骰子得两个数, 记为$a$、$b$, 设$d=|a-b|$, 分别计算$d$的各个值出现的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018740": {
+        "id": "018740",
+        "content": "阅读下列材料, 写一篇$300$字的文章, 谈谈你对生活中的概率的认识.\\\\\n\\begin{center}{\\it ``黄金$72$小时''}\\end{center}\n{\\it 地震等地质灾害发生后, 在媒体上经常可以看到``黄金$72$小时''这几个字. 你知道它表示的是什么意思吗?\\\\\n医学研究和统计表明, 在没有食物尤其是没有水的条件下, 生命的存续期一般不会超过$3$天. 国际教援界认为, 在地震等地质灾害发生后的$72$小时内, 被救出人员的存活率随时间的消逝呈递减趋势: 第一天(即$24$小时内), 存活率约为$90 \\%$; 第二天, 存活率为$50 \\%-60 \\%$; 第三天, 存活率为$20 \\%-30 \\%$. 再往后的话, 存活率将进一步减少.\\\\\n这里的存活率可以用概率来理解: 被救出的人员, 如果是在$24$小时内被发现的, 那么该人员生还的概率为$90 \\%$; 如果是在第$24-48$小时内被发现的, 那么生还的概率为$50 \\%-60 \\%$; 如果是第$48-72$小时内发现的, 那么生还的概率为$20 \\%-30 \\%$. 这就意味着, 当地震等地质灾害发生后, 应该``与时间赛跑'', 利用各种手段和机会尽可能早地发现被困人员.\\\\\n需要注意的是, 概率描述的只是事件发生的可能性大小, 发生的可能性小(即概率小)并不代表不会发生. 统计数据表明, 地震六天后, 被埋人员生还的概率几乎为零. 但是这样的事例并不是没有: 2005 年巴基斯坦$7.6$级地震中, 一名青年被埋$27$天后获救生还; 2008 年我国汶川地震中, 一位$60$岁的老人被困$11$天后获救生还; 等等. 因此, 几乎所有的救援工作, 在``黄金$72$小时''之外都会继续, 以便发现更多生命的奇迹.}",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018741": {
+        "id": "018741",
+        "content": "从分别写有$A$、$B$、$C$的三个大小与质地相同的球中任意取两个, 寻找其等可能的样本空间.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018742": {
+        "id": "018742",
+        "content": "从一个放有大小与质地相同的两个白球、一个黑球的罐子中任意摸两个球, 写出其样本空间并思考: 这个样本空间是否有不同的写法? 什么样的样本空间有等可能性? 并求至少摸到一个黑球的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018743": {
+        "id": "018743",
+        "content": "甲、乙两个人玩``石头、剪刀、布''的游戏, 假设两人都随机出拳, 求:\\\\\n(1) 平局的概率;\\\\\n(2) 甲赢的概率;\\\\\n(3) 甲不输的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018744": {
+        "id": "018744",
+        "content": "将一枚均匀的硬币投掷$3$次, 则正面出现的次数比反面出现的次数多的概率是\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "018745": {
+        "id": "018745",
+        "content": "一个盒子中装有标号为$1$、$2$、$3$、$4$、$5$的$5$张标签, 按先后顺序任取$2$张标签, 每次取出后不放回, 求取出的$2$张标签上的数字为相邻整数的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018746": {
+        "id": "018746",
+        "content": "某号码锁从左往右有六个拨盘, 每个拨盘上有从$0$到$9$共$10$个数字, 当六个拨盘从左往右的六个数字号码是$907856$时, 锁才能打开.\n(1) 如果某人记不得密码, 则一次打开锁的概率是多少?\\\\\n(2) 如果某人只记得密码最后两位是$56$, 则他一次打开锁的概率是多少?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018747": {
+        "id": "018747",
+        "content": "齐王与田忌赛马, 田忌的上等马优于齐王的中等马, 劣于齐王的上等马; 田忌的中等马优于齐王的下等马, 劣于齐王的中等马; 田忌的下等马劣于齐王的下等马. 现齐王与田忌各出上等马、中等马、下等马一匹, 进行三场比赛, 每场双方均任意选一匹马参赛, 胜两场或两场以上的人获胜, 求田忌获胜的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018748": {
+        "id": "018748",
+        "content": "掷两颗骰子, 观察掷得的点数. 设$A$: 至少一个是偶数, $B$: 至少一个是奇数, $C$: 两个点数的乘积是偶数, $D$: 两个点数的和是奇数. 讨论:\\\\\n(1) $A$与$B$的关系;\\\\\n(2) $A$与$C$的关系;\\\\\n(3) $A$、$B$、$D$之间的关系;\\\\\n(4) $C$与$D$的关系.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018749": {
+        "id": "018749",
+        "content": "掷两颗骰子, 观察掷得的点数. 设$A$: 至少一个点数是偶数, $B$: 点数之和是偶数. 求:\\\\\n(1) $A \\cap B$;\\\\\n(2) $A \\cup B$.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018750": {
+        "id": "018750",
+        "content": "掷一颗均匀的骰子, 用$A$表示事件``向上的点数至少为$5$'', 则$\\overline {A}$指事件\\blank{50}, $\\overline {A}$的对立事件为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "018751": {
+        "id": "018751",
+        "content": "从一副扑克牌 (去掉大、小王, 共$52$张) 中随机选取1张, 下列每组事件是否是互斥事件? 若是互斥事件, 那么是否互为对立事件?\\\\\n(1) $C$: 这张牌花色是红心, $D$: 这张牌花色是方块;\\\\\n(2) $C$: 这张牌牌面是$2,3,4,5,6,7,8,9,10$之一, $D$: 这张牌牌面是J,Q,K,A之一;\\\\\n(3) $C$: 这张牌牌面是$2,3,4,5,6,7$之一且花色为方块, $D$: 这张牌牌面是8,9,10,J,Q,K,A之一且花色为方块.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018752": {
+        "id": "018752",
+        "content": "设$A$与$B$是同一样本空间中的两个事件, ``$A$与$B$相互对立''是``$A$与$B$互斥''的什么条件? 说明理由.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018753": {
+        "id": "018753",
+        "content": "设$A$、$B$为两个事件, 试用$A$、$B$表示下列各事件:\\\\\n(1) $A$、$B$两个事件中至少有一个发生;\\\\\n(2) 事件$A$发生且事件$B$不发生;\\\\\n(3) $A$、$B$两个事件中恰有一个不发生.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018754": {
+        "id": "018754",
+        "content": "已知事件$A$与$B$互斥, 判断$\\overline {A}$与$B$的关系, 以及$\\overline {A}$与$\\overline {B}$的关系, 说明理由.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018755": {
+        "id": "018755",
+        "content": "小明在书店随机地选一本书, 设事件$A$: 小明选的书是数学书, 事件$B$: 小明选的书是中文版的书, 事件$C$: 小明选的书是$2020$年或$2020$年以后出版的书.\\\\\n(1) 写出$A \\cap B \\cap \\overline {C}$表示的事件;\\\\\n(2) 在什么情况下, $A \\cap B \\cap C=A$成立? 说明理由;\\\\\n(3) 在什么情况下, $\\overline {C} \\subseteq B$成立? 说明理由;\\\\\n(4) $\\overline {A}=B$的含义是否是``书店中所有的数学书都不是中文版的''? 说明理由.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018756": {
+        "id": "018756",
+        "content": "抛掷三枚硬币, 求:\\\\\n(1) 至少出现两个正面的概率;\\\\\n(2) 至少出现一个正面的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018757": {
+        "id": "018757",
+        "content": "甲、乙两人下棋, 甲获胜的概率为$0.4$, 甲不输的概率为$0.9$, 求甲、乙两人下成和棋的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018758": {
+        "id": "018758",
+        "content": "甲、乙各抛掷若干枚硬币, 甲抛掷的硬币总数恰比乙少一枚. 求甲得到的正面数比乙得到的正面数少的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018759": {
+        "id": "018759",
+        "content": "已知某次足球比赛中, 一学校足球队赢的概率为$0.7$, 打平的概率为$0.2$, 求该学校足球队不输的概率与输球的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018760": {
+        "id": "018760",
+        "content": "掷$3$颗骰子, 求所得点数之和不小于$5$的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018761": {
+        "id": "018761",
+        "content": "设$A$、$B$是同一样本空间中的两个事件, 探索$P(A \\cup B)$, $P(A)$, $P(B)$, $P(A \\cap B)$之间的等量关系, 并说明理由.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018762": {
+        "id": "018762",
+        "content": "甲、乙各抛掷$n$枚硬币, 证明: ``甲得到的正面数比乙得到的正面数少''这一事件的概率小于$\\dfrac{1}{2}$.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018763": {
+        "id": "018763",
+        "content": "某药物公司实验一种降低胆固醇的新药, 在$500$个病人中进行实验, 结果如下表所示.\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline 胆固醇降低的人数 & 没有起作用的人数 & 胆固醇升高的人数\\\\\n\\hline 307 & 120 & 73 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n求下列事件的经验概率:\\\\\n(1) 使用药物后胆固醇降低;\\\\\n(2) 使用药物后没有起作用;\\\\\n(3) 使用药物后胆固醇升高.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018764": {
+        "id": "018764",
+        "content": "一个袋子中装有$5$个大小和质地都相同的小球, 其中$2$个黑色, $3$个不是黑色. 每次从袋子中抽取$1$个小球, 观察颜色后再放回袋中, 摇匀后抽取下一次. 共抽取$3$次. 设计一个随机试验, 计算恰好出现$1$次黑球的经验概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018765": {
+        "id": "018765",
+        "content": "某篮球运动员的投篮命中率为$80 \\%$. 对此, 某同学这样理解: 这名运动员如果投篮$100$次, 则一定有$80$次投中. 这种理解对吗? 为什么?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018766": {
+        "id": "018766",
+        "content": "某袋子内装有三种颜色的小球, 小明每次从袋子中随机摸出一个小球, 观察颜色后再放回, 重复了$90$次, 得到的信息如下: 观察到红色小球$52$次、 蓝色小球$26$次. 如果从这个袋子内任意摸一个小球, 试求:\\\\\n(1) 这个小球是红色的经验概率;\\\\\n(2) 这个小球既不是红色也不是蓝色的经验概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018767": {
+        "id": "018767",
+        "content": "一个地区从某年起$4$年之内的新生婴儿数以及其中的女婴数如下表所示, 其中部分数据缺失.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline 时间 & 1 年内 & 2 年内 & 3 年内 & 4 年内 \\\\\n\\hline 新生婴儿数 &$?$& 9607 & 13518 & 17190 \\\\\n\\hline 女婴数 & 2370 &$?$& 6992 & 8892 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 计算``4 年内新生婴儿中, 性别为女''的频率; (结果精确到$0.001$)\\\\\n(2) 已知这$4$年内, 每年女婴出生的频率非常稳定. 试估计上述表格中缺失的各个数据.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018768": {
+        "id": "018768",
+        "content": "阅读教材第$110-111$页《蒙特卡洛算法》的相关内容, 并完成以下问题.\\\\\n第$24$届冬季奥林匹克运动会由北京和张家口共同举办, 所有的冰上项目在北京进行, 北京成为了第一个同时举办夏季与冬季奥运会的城市. 有一张该届冬奥会的宣传彩页, 大小为$210 \\mathrm{mm} \\times 297 \\mathrm{mm}$(A4 纸). 其中的卡通图像是冬奥会吉祥物之一: 雪容融.\n请基于蒙特卡洛算法, 设计一个试验, 估算该张彩页中``雪容融''的面积.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018769": {
+        "id": "018769",
+        "content": "抛掷$10$枚硬币, 求:\\\\\n(1) 都是正面朝上的概率;\\\\\n(2) 恰有$1$枚反面朝上的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018770": {
+        "id": "018770",
+        "content": "两个人比赛, 对于弱者(赢的概率较小者)来说, 一局定胜负和三局两胜比较, 哪个更有利? (这里所说的``三局两胜''是常见的比赛模式, 指先赢得两局者为胜, 最多三局结束)",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018771": {
+        "id": "018771",
+        "content": "某种细胞若不能分裂则死亡, 并且一个细胞死亡和分裂为两个细胞的概率都为$\\dfrac{1}{2}$, 每次分裂结果互不影响. 现有一个这样的细胞, 求这个细胞两次分裂后仍有细胞存活的概率是多少?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018772": {
+        "id": "018772",
+        "content": "甲、乙两名运动员进行单打比赛, 已知每一局甲获胜的概率为$0.6$, 每局两人输赢互不影响, 各局结果也互不影响. 比赛可以采用三局两胜制或五局三胜制, 问: 在哪一种赛制下甲获胜的可能性大.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018773": {
+        "id": "018773",
+        "content": "判断下列事件$A$与$B$是否相互独立?\\\\\n(1) 从一副去掉大小王的$52$张扑克牌中随机抽取一张牌, 事件$A$表示``取得的牌面数是10'', 事件$B$表示``取得的牌的花色是红桃'';\\\\\n(2) 掷一颗骰子, 事件$A$表示``结果是偶数'', 事件$B$表示``结果是奇数'';\\\\\n(3) 掷一颗骰子, 事件$A$表示``结果是奇数'', 事件$B$表示``结果是整数'';\\\\\n(4) 掷一颗骰子, 事件$A$表示``结果是偶数'', 事件$B$表示``结果是无理数''.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018774": {
+        "id": "018774",
+        "content": "证明: 如果两个事件$A$与$B$独立, 那么事件$A$与$\\overline {B}$也独立.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018775": {
+        "id": "018775",
+        "content": "两个篮球运动员甲和乙罚球时命中的概率分别是$0.7$和$0.6$, 两人各投一次, 假设事件``甲命中''与``乙命中''是独立的, 求至少一人命中的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018776": {
+        "id": "018776",
+        "content": "$A$、$B$两人下棋, 每局两人获胜的可能性一样. 某一天两人要进行一场三局两胜的比赛, 最终胜者赢得$100$元奖金, 第一局比赛$A$胜, 后因为有其他事而要中止比赛. 问: 怎么分$100$元奖金才公平?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018777": {
+        "id": "018777",
+        "content": "求证: 如果两个事件$A$与$B$独立, 那么事件$\\overline {A}$与$\\overline {B}$也独立.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018778": {
+        "id": "018778",
+        "content": "某型号高射炮发射一枚炮弹击中目标的概率为$0.6$. 在某次演习活动中, 若干门此型号高射炮同时发射一发炮弹射击目标, 每门炮击中目标是相互独立的, 欲击中目标的概率超过$0.99$, 至少需要多少门该型号的高射炮?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018779": {
+        "id": "018779",
+        "content": "一个袋子中装有$2$个红色小球和$3$个白色小球(球的大小与质地均相同), 任取$2$个小球.\\\\\n(1) 一次取出两个小球. 分别求以下两个事件的概率:\\\\\n(I) 取出的$2$个小球全是红球;\\\\\n(II) 取出的$2$个小球不全是红球;\\\\\n(2) 分两次取, 每次任取$1$个小球. 记事件$C$: $2$个小球中至少有$1$个是红球, 分别求满足下列条件的事件$C$的概率;\\\\\n(1) 第一次取出的球不放回, 第二次再取;\\\\\n(2) 第一次取出球后放回袋中搅匀, 第二次再取.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018780": {
+        "id": "018780",
+        "content": "一个袋子中装有$2$个红色小球和$3$个白色小球(球的大小与质地均相同), 往这个袋子里添加若干个相同的白球. 先后两次取球, 每次任取$1$个小球. 第一次取出球后放回袋中搅匀, 第二次再取. 若要将事件$C$的概率减小到不足$0.3$, 试问至少需要添加几个白球?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018781": {
+        "id": "018781",
+        "content": "射击队某位手枪选手在训练时射击命中环数的频率如下表所示.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline 命中环数 & 7 & 8 & 9 & 10 \\\\\n\\hline 频率 & 0.04 & 0.12 & 0.33 & 0.46 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 根据上表数据, 是否意味着该选手在将来的某次训练中射击$100$次, 则一定有$46$次命中$10$环?\\\\\n(2) 求该选手射击一次, 命中不足$8$环的经验概率;\\\\\n(3) 在某次资格赛中, 该选手只要在最后两轮的射击中(每轮射击一次, 两次射击结果互不影响) 命中环数之和不少于$19$环就可赢得比赛. 试估计该选手赢得比赛的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018782": {
+        "id": "018782",
+        "content": "有一款新的益智对弈游戏. 根据规则, 每玩一局则对弈双方必定有$1$人胜利、$1$人失败. 判断游戏是否公平的标准是对弈双方胜利的概率是否相等. 甲乙两人是好朋友, 平时经常一起玩各类益智游戏且水平相当. 乙来邀请甲一起玩这款新游戏. 以下是甲在$3$个月内的胜负情况:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline 时间 & 初始$2$天 & 1 个月内 & 3 个月内 \\\\\n\\hline 局数 & 10 & 102 & 311 \\\\\n\\hline 甲胜利的局数 & 5 & 30 & 72 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n请你用学过的概率知识分析表格内数据, 并说一说这款游戏是否公平?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "018783": {
+        "id": "018783",
+        "content": "运动员甲和运动员乙将进行一场三局两胜的羽毛球比赛. 若每局比赛甲获胜的概率为$0.6$, 乙获胜的概率为$0.4$. 请利用教材第$174$页的随机数表进行模拟试验, 估计甲赢得比赛的概率. (结果精确到$0.01$)",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第三册概率初步例题与习题",
+        "edit": [
+            "20230706\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "020001": {
         "id": "020001",
         "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",