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 67130a26..46013f60 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 = 19118 #起始id设置, 来自"寻找空闲题号"功能
+starting_id = 19192 #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 a191d64f..77a29b4c 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -491901,6 +491901,1260 @@
         "space": "4em",
         "unrelated": []
     },
+    "019192": {
+        "id": "019192",
+        "content": "掷一颗骰子并观察出现的点数. 已知出现的点数不超过$3$, 求出现的点数是奇数的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019193": {
+        "id": "019193",
+        "content": "一个家庭有两个孩子, 假设生男孩和生女孩是等可能的, 在这个家庭有女孩的条件下, 分别求两个孩子是一个男孩和一个女孩以及两个孩子都是女孩的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019194": {
+        "id": "019194",
+        "content": "一个罐子中有大小与质地相同的黑、白、红三个球, 不放回地摸球. 求:\\\\\n(1) 在第一次没有摸到黑球的条件下, 第二次也没有摸到黑球的概率;\\\\\n(2) 两次都没有摸到黑球的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019195": {
+        "id": "019195",
+        "content": "在标有$1$、$2$、$3$、$4$、$5$的五张卡片中依次选取两张, 在第一张是奇数的条件下, 求第二张也是奇数的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019196": {
+        "id": "019196",
+        "content": "一个袋子中装有$10$个大小与质地相同的小球, 其中有$2$个红球、 $3$个白球、$5$个黑球. 现从中摸$2$个球, 已知摸到的都不是红球, 求摸到的都是黑球的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019197": {
+        "id": "019197",
+        "content": "已知某校的午餐由``主食''与``配菜''两部分组成, 主食和配菜均有若干种不同的选择. 某个学期的统计结果显示, 学生购买主食$A$的概率为$25 \\%$, 而在购买主食$A$的学生中, 又有$70 \\%$的学生会购买配菜$B$作为搭配, 求学生同时购买主食$A$与配菜$B$的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019198": {
+        "id": "019198",
+        "content": "已知$P(A)=0.4, P(B | A)=0.75$, 求$P(\\overline {B} | A)$以及$P(\\overline {B} \\cap A)$.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019199": {
+        "id": "019199",
+        "content": "一个袋子中装有大小与质地相同的$2$个红球和$4$个白球, 甲乙两人依次无放回地摸球, 约定摸到白球则换人摸球, 并由甲先摸球. 求第二次由乙摸球且摸到红球的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019200": {
+        "id": "019200",
+        "content": "假设一个袋子中装有大小与质地相同的$3$个白球、$2$个黑球, 五个人依次不放回地摸球, 分别求第二、第三个人摸到白球的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019201": {
+        "id": "019201",
+        "content": "设有两个罐子, $A$罐中放有$2$个白球、$1$个黑球, $B$罐中放有$3$个白球, 这些球的大小与质地相同. 现在从两个罐子中各摸$1$个球并交换, 求这样交换$2$次后, 黑球还在$A$罐中的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019202": {
+        "id": "019202",
+        "content": "已知$P(A)=0.7$, $P(B | A)=0.5$, $P(B | \\overline {A})=0.4$, 求$P(B)$.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019203": {
+        "id": "019203",
+        "content": "根据长期观察, 如果某天下雨, 甲去小区绿地散步的概率为$0.3$; 如果某天不下雨, 甲去小区绿地散步的概率为$0.8$. 已知明天降水的概率是$40 \\%$, 求甲去小区绿地散步的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019204": {
+        "id": "019204",
+        "content": "甲、乙两个袋子中装有大小与质地相同的小球, 甲袋中有$6$个红球、 $4$个白球; 乙袋中装有$8$个红球、$6$个白球. 现从两个袋子中等可能地随机选取一个袋子, 再从选出的袋子中随机摸出$2$个球, 求摸出的$2$个球都是红球的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019205": {
+        "id": "019205",
+        "content": "某地市场上, 某商品主要有甲、乙两种品牌, 已知甲的市场占有率为$45 \\%$, 乙的市场占有率为$50 \\%$, 剩余品牌的占有率为$5 \\%$. 已知甲品牌一等品比例为$90 \\%$, 乙品牌一等品的比例为$95 \\%$, 剩余品牌一等品的比例为$80 \\%$. 现在该地市场上任取一件该商品, 求它是一等品的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019206": {
+        "id": "019206",
+        "content": "设$A$、$B$是互斥事件, $P(A)=P(B)=0.4$, $P(C | A)=0.5$, $P(C | B)=0.4$, 如果事件$C$发生时, 事件$A$、$B$至少有一个发生, 求$P(C)$.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019207": {
+        "id": "019207",
+        "content": "某通信实验中, 信号发射方随机地通过$U_1$、$U_2$两个信道之一将信号发射给接收方, 由于存在信号干扰, 信号可能无法被接收方收到. 已知$U_1$、$U_2$信道发送信号被接收到的成功率分别为$95 \\%$、$90 \\%$. 假设选择$U_1$、$U_2$发送信号是等可能的. 已知某次实验中接收方成功地接收到了信号, 求信号由信道$U_1$发送的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019208": {
+        "id": "019208",
+        "content": "假设某产品的一个部件来自三个供应商, 供货占比分别是$\\dfrac{1}{2}$、$\\dfrac{1}{6}$、$\\dfrac{1}{3}$, 而它们的良品率分别是$0.96$、$0.90$、$0.93$. 现在某件成品因为该部件的问题导致了一定的经济损失, 但由于部件损毁, 无法获知该部件究竟来自于哪一个供应商. 在此条件下, 试问: 每个供应商应承担经济损失中的多少才合理?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019209": {
+        "id": "019209",
+        "content": "已知$P(A | B)=0.5$, $P(A | \\overline {B})=0.4, P(B)=0.7$, 求$P(B | A)$.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019210": {
+        "id": "019210",
+        "content": "在$A$、$B$、$C$三个地区爆发了流感, 这三个地区分别有$6 \\%$、$5 \\%$、$4 \\%$的人患了流感. 假设这三个地区的人口数之比为$5: 7: 8$, 现从这三个地区中任意选取一个人, 如果此人患有流感, 求此人选自地区$A$的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019211": {
+        "id": "019211",
+        "content": "甲、乙两个袋子中装有大小与质地相同的小球, 甲袋中有$6$个红球、 $4$个白球; 乙袋中装有$8$个红球、$6$个白球. 现等可能地从两个袋子中随机选取一个袋子, 再从选出的袋子中摸出一个球, 若摸出的球是红球, 求它来自牛甲袋的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019212": {
+        "id": "019212",
+        "content": "袋中装有大小与质地相同的$4$个红球与$8$个白球. 从中依次摸两个球, 规则如下: 先从袋中任取一个球, 若该球是红球, 则放回袋中, 进行下一次摸球; 若该球是白球, 则不放回, 直接进行下一次摸球. 求第二次摸到白球的条件下, 第一次摸到白球的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019213": {
+        "id": "019213",
+        "content": "掷一颗骰子, 观察掷得的点数.\\\\\n(1) 求点数$X$的分布;\\\\\n(2) 只关心点数$6$是否出现. 若出现, 则记$Y=1$, 否则记$Y=0$. 求$Y$的分布.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019214": {
+        "id": "019214",
+        "content": "统计某地历史上近两百年的年降水量, 得到以下数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline 年降水量 $/ \\mathrm{mm}$ & {$[0,100]$} & $(100,200]$ & $(200,300]$ & $(300,400]$ & $400$ 以上 \\\\\n\\hline 年数 & 10 & 55 & 85 & 35 & 15 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n请据此构造一个随机变量并求其分布.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019215": {
+        "id": "019215",
+        "content": "设某项试验的成功率是失败率的$3$倍, 用随机变量$X$去描述$1$次试验的成功次数, 则$P(X=1)=$\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019216": {
+        "id": "019216",
+        "content": "甲、乙两班进行足球对抗赛, 每场比赛赢了的队伍得$3$分, 输了的队伍得$0$分, 平局的话, 两队各得$1$分, 共进行三场. 用$X$表示甲的得分, 则$X=3$表示\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019217": {
+        "id": "019217",
+        "content": "设$q$为常数, 若随机变量$X$的分布为$\\begin{pmatrix} -1 & 0 & 1 \\\\ \\dfrac{1}{2} & 1-2 q & q^2\\end{pmatrix}$, 则$q=$\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019218": {
+        "id": "019218",
+        "content": "从一个放有大小与质地相同的$5$个白球、$5$个黑球的罐子中随机摸出$3$个球, 摸得$1$个白球记$2$分, 摸得$1$个黑球记$1$分, 求得分$X$的分布.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019219": {
+        "id": "019219",
+        "content": "设随机变量$X$的分布为$\\begin{pmatrix}1 & 2 & 3 & 4 & 5 \\\\ a_1 & a_2 & a_3 & a_4 & a_5\\end{pmatrix}$, 其中$a_1, a_2, a_3, a_4$, $a_5$成等差数列, 则$a_1 a_5$的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019220": {
+        "id": "019220",
+        "content": "2021 年上海全年的空气质量指数 (AQI) 数据如下:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline 空气质量指数 AQI & {$[0,50]$} & $(50,100]$ & $(100,150]$ & $(150,200]$ & $(200,300]$ \\\\\n\\hline 频数 & 244 & 112 & 8 & 0 & 1 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n据此数据, 请查阅相关资料, 构造一个随机变量并求其分布.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019221": {
+        "id": "019221",
+        "content": "抛掷$n$枚硬币, 用$X$表示正面朝上的硬币数. 求它的分布及期望.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019222": {
+        "id": "019222",
+        "content": "根据气象预报, 某地区近期有小洪水的概率为$0.25$, 有大洪水的概率为$0.01$. 该地区某工地上有一台大型设备, 遇到大洪水时要损失$60000$元, 遇到小洪水时要损失$10000$元. 为保护设备, 有以下$3$种方案:\\\\\n方案 1: 暂时运走设备, 来回搬运费为$3800$元.\\\\\n方案 2: 建一临时保护围墙, 建造及拆除费为$2000$元, 但围墙只能防小洪水.\\\\\n方案 3: 不采取措施, 希望不发生洪水.\\\\\n你会选择哪一种方案呢?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019223": {
+        "id": "019223",
+        "content": "若随机变量$X$的分布为$\\begin{pmatrix}0 & 1 \\\\ 0.3 & 0.7\\end{pmatrix}$, 则随机变量$10X+3$的期望$E[10X+3]=$\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019224": {
+        "id": "019224",
+        "content": "某学校要从$5$名男生和$2$名女生中随机选出$2$人作为志愿者, 若用随机变量$X$表示选出的志愿者中女生的人数, 求$X$的分布与期望.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019225": {
+        "id": "019225",
+        "content": "马老师从课本上抄录一个随机变量$X$的分布$\\begin{pmatrix} 1 & 2 & 3 \\\\ ? & ! & ?\\end{pmatrix}$, 请小明同学计算$X$的期望. 尽管``$!$''处完全无法看清, 且两个`$?$''处字迹模糊, 但能断定这两个``$?$''处的数值相同. 据此, 小明给出了正确答案$E[X]=$\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019226": {
+        "id": "019226",
+        "content": "一接待中心有$A$、$B$、$C$三部热线电话. 已知某一时刻电话$A$、$B$占线的概率均为$0.5$, 电话$C$占线的概率为$0.4$, 各部电话是否占线相互之间没有影响. 假设该时刻有$X$部电话占线, 求$X$的期望.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019227": {
+        "id": "019227",
+        "content": "掷一颗骰子, 用$X$表示䣏得的点数. 求$X$的方差.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019228": {
+        "id": "019228",
+        "content": "掷两颗骰子, 掷得的点数分别为$X$、$Y$. 求点数和$X+Y$与点数差$X-Y$的期望与方差.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019229": {
+        "id": "019229",
+        "content": "某人有一笔$10$万元的闲置资金, 可以进行为期一年的投资. 可以直接存入银行, 假定银行同期年利率为$1.75 \\%$, 还有两种投资方案可供选择, 方案所得收益为$X$(单位: 万元), 方案三所得收益为$Y$(单位: 万元). 已知$X$的分布为$\\begin{pmatrix}-2 & 8 \\\\ 0.7 & 0.3\\end{pmatrix}$, $Y$的分布为$\\begin{pmatrix}-3 & 12 \\\\ 0.7 & 0.3\\end{pmatrix}$, 若该投资人征求你的意见, 你会给出怎样的建议?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019230": {
+        "id": "019230",
+        "content": "独立地重复$n$次成功概率为$p$的伯努利试验, 求至少有一次成功的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019231": {
+        "id": "019231",
+        "content": "设$X$服从二项分布$B(n, p)$, 求$X$的期望与方差.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019232": {
+        "id": "019232",
+        "content": "甲、乙两选手进行围棋比赛, 假设每局比赛是相互独立的. 如果每局比赛甲获胜的概率为$0.6$, 那么采用$3$局$2$胜制还是采用$5$局$3$胜制对甲更有利? 为什么?",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019233": {
+        "id": "019233",
+        "content": "如果一袋中装有大小与质地相同的$a$个白球、$b$个黑球, 依次随机且不放回地取$n$个球, 用$X$表示其中的白球数. 求$E[X]$的值.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019234": {
+        "id": "019234",
+        "content": "设袋中装有大小与质地相同的$6$个白球、$4$个黑球. 现在依次随机且不放回地摸$5$个球, 用$X$表示摸出的白球个数. 求$D[X]$的值.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019235": {
+        "id": "019235",
+        "content": "某批产品总数为$1000$件, 其中有不合格品$10$件. 现从这批产品中任意抽取$5$件, 用$X$表示取出的产品中不合格品的件数, 分别在放回抽取与否放回抽取方式下求$P(X=2)$的值.(结果精确到 0.000001 )",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019236": {
+        "id": "019236",
+        "content": "某校高三(1)班的联欢会上设计了一项游戏: 在一个口袋中装有大小与质地相同的$10$个红球和$20$个白球. 一次从中摸出$5$个球, 摸到$4$个红球和$1$个白球的就获一等奖, 用随机变量$X$表示取到的红球数.\\\\\n(1) 求获一等奖的概率;\\\\\n(2) 求$E[X]$的值.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019237": {
+        "id": "019237",
+        "content": "设袋中装有大小与质地相同的$4$个白球、 $3$个黑球. 随机地从袋中取出$4$个球. 设取到一个白球得$2$分, 取到一个黑球得$1$分, 用$X$表示取出的球的得分总数, 求$E[X]$和$D[X]$的值.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019238": {
+        "id": "019238",
+        "content": "某公司生产的糖果每包标识质量是$500 \\mathrm{g}$, 但公司承认实际质量存在误差. 已知每包糖果的实际质量服从$\\mu=500$、$\\sigma^2=2.5^2$的正态分布. 问: 随意买一包该公司生产的糖果, 其质量误差超过$5 \\mathrm{g}$(即$1 \\%$)的可能性有多大?(结果精确到$0.1 \\%$)",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019239": {
+        "id": "019239",
+        "content": "设$X$为任取的某袋有包装误差的产品的质量, $X \\sim N(\\mu, \\sigma^2)$. 分别求$|X-\\mu|<\\sigma$, $|X-\\mu|<2 \\sigma$及$|X-\\mu|<3 \\sigma$的概率. (结果精确到$0.1 \\%$)",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019240": {
+        "id": "019240",
+        "content": "已知随机变量$X$服从正态分布$N(\\mu, \\sigma^2)$($\\sigma>0$), 且$P(X \\leq c)=P(X>c)$, 则$c$的值为\\bracket{20}.\n\\fourch{$0$}{$\\sigma$}{$-\\mu$}{$\\mu$}",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019241": {
+        "id": "019241",
+        "content": "设两个正态分布$N(\\mu_1, \\sigma_1^2)$($\\sigma_1>0$)和$N(\\mu_2, \\sigma_2^2)$($\\sigma_2>0$)的正态密度函数图像如图所示, 则\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -4:4,samples = 300] plot (\\x,{1/0.2/sqrt(2)/sqrt(pi)*exp(-pow(\\x+1,2)/2/0.2/0.2)});\n\\draw (-1,2) node [above] {$N(\\mu_1,\\sigma_1^2)$};\n\\draw [domain = -4:4,samples = 300] plot (\\x,{1/0.5/sqrt(2)/sqrt(pi)*exp(-pow(\\x-0.5,2)/2/0.5/0.5)});\n\\draw (0.5,1) node [above,fill = white] {$N(\\mu_2,\\sigma_2^2)$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$\\mu_1<\\mu_2$, $\\sigma_1<\\sigma_2$}{$\\mu_1<\\mu_2$, $\\sigma_1>\\sigma_2$}{$\\mu_1>\\mu_2$, $\\sigma_1<\\sigma_2$}{$\\mu_1>\\mu_2$, $\\sigma_1>\\sigma_2$}",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019242": {
+        "id": "019242",
+        "content": "已知随机变量$X$服从正态分布$N(\\mu, \\sigma^2)$($\\sigma>0$), 求$P(\\mu \\leq X<\\mu+\\sigma)$的值. (结果精确到$0.1 \\%$)",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019243": {
+        "id": "019243",
+        "content": "已知某批零件的长度误差 (单位: 毫米) 服从正态分布$N(0,3^2)$, 从中随机取一件, 求长度误差落在区间$(3,6)$内的概率. (结果精确到$0.1 \\%$)",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019244": {
+        "id": "019244",
+        "content": "已知随机变量$X$服从正态分布$N(2, \\sigma^2)$($\\sigma>0$), 且$P(X<4)=a$, 求$P(X<0)$. (用$a$表示)",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019245": {
+        "id": "019245",
+        "content": "某批待出口的水果罐头每罐净重$X$(单位: $\\mathrm{g}$)服从正态分布$N(184,2.5^2)$, 求:\\\\\n(1) 随机抽取一罐, 其净重不小于$191.5 \\mathrm{g}$的概率;\\\\\n(2) 随机抽取一罐, 其净重在$179 \\mathrm{g}$与$189 \\mathrm{g}$之间的概率.(结果精确到$0.1 \\%$)",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019246": {
+        "id": "019246",
+        "content": "口袋里装有大小与质地相同的$4$个红球和$8$个白球, 甲、乙两人从袋中摸球, 每次摸$1$个球.\\\\\n(1) 若甲、乙两人无放回地摸球, 由甲先摸$1$个球, 乙再摸$1$个球, 求甲摸到白球的条件下, 乙摸到红球的概率;\\\\\n(2) 若甲、乙两人无放回地摸球, 并由甲先摸$1$个球, 乙再摸$1$个球, 求甲摸到白球且乙摸到红球的概率;\\\\\n(3) 由甲每次摸球后都放回地摸球三次, 用$X$表示三次摸球中摸到红球的次数, 求$X$的分布、期望与方差;\\\\\n(4) 由甲无放回地摸球三次, 用$X$表示三次摸球中摸到红球的次数, 求$X$的分布与期望;\\\\\n(5) 制定规则如下: 若一方摸出$1$个红球, 则此人继续下一次摸球, 若一方摸出$1$个白球, 则由对方接替下一次摸球, 由甲进行第一次摸球.\\\\\n(I) 若甲、乙两人无放回地摸球, 求第三次仍由甲摸球的概率;\\\\\n(II) 若甲、乙两人每次摸球后都放回地摸球, 求在前两次摸球中, 甲摸得的红球次数$X$的分布及期望;\\\\\n(III) 在(II)的条件下, 如果规定摸到红球得$3$分, 摸到白球得$1$分, 求在两次摸球中, 甲得分的期望.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019247": {
+        "id": "019247",
+        "content": "通勤时间是指单日内某人从居住地到工作地的用时. 数学曾老师经过若干个月的统计发现, 其通勤时间$X$(单位: 分钟) 服从正态分布$N(\\mu, \\sigma^2)$.\\\\\n(1) 如果$P(X \\geq 40)=P(X \\leq 20)$, 那么曾老师通勤时间的均值为多少?\\\\\n(2) 设$\\mu=40$, 如果曾老师在某月的$22$天工作日中, 通勤时间在$40$分种至$60$分钟之间的天数有$8$天, 那么这个月中她通勤时间不超过$20$分钟的天数大约是多少?\\\\\n(3) 设$\\mu=40$, $\\sigma=4$. 曾老师某天$7$点$10$分出门, 如果学校要求在$8$点前到达, 那么曾老师当天迟到的概率约为多少? (结果精确到$0.1 \\%$. 参考数据: $\\Phi(2) \\approx 0.9772$, $\\Phi(2.5) \\approx 0.9938$, $\\Phi(3) \\approx 0.9987$.)",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019248": {
+        "id": "019248",
+        "content": "某校桥牌社每个月要和兄弟学校的桥牌社进行一次友谊赛, 为此要从$7$名社员中随机选择$2$名参加友谊赛. 新学年友谊赛从$10$月份开始, 此时$7$名社员中有$3$名新社员没有参加过此前的友谊赛.\\\\\n(1) 设$10$月份参加比赛的新社员的人数为$X$, 求$X$的分布与期望;\\\\\n(2) 求$11$月份参加比赛的社员中, 恰有$1$个没有友谊赛经验的概率.",
+        "objs": [],
+        "tags": [
+            "第八单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂选择性必修第二册概率初步续例题与习题",
+        "edit": [
+            "20230707\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.",