这部分需要会什么？
- 从等可能结果或频数表计算概率
- 正确确定条件概率的分母
- 区分互斥、独立和重复计算
核心概念与公式
等可能情形下，概率为有利结果数除以总结果数。条件概率 \(P(A\mid B)=P(A\cap B)/P(B)\)，要求 \(P(B)>0\)；“已知 B”意味着只在 B 发生的结果中比较。
并集公式为 \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)。独立事件满足 \(P(A\cap B)=P(A)P(B)\)；互斥事件不能同时发生。两个概率都大于零的互斥事件不会独立。
做题时怎样使用
- 确定抽取规则与样本空间，检查结果是否等可能
- 出现“given”“among”等条件时，先缩小分母范围
- 涉及“或”时扣除重复部分，涉及“且”时检查是否真的独立
容易混淆的地方
从表中求“在女生中选择某课程的比例”，分母是女生人数，不是全体人数。不放回抽样一般会改变后续概率。
用一个例题串起方法
知识点教学例题共有 60 人，其中女生 36 人；女生中有 15 人参加社团。从女生中随机选一人，该人参加社团的概率是多少？
展开解题思路 ＋
条件已限定为女生，所以概率为 \(15/36=5/12\)，不能使用 \(15/60\)。
本知识点题库
先独立作答，再查看答案与解析。
概率与条件概率进阶
A box contains 23 red buttons and 27 blue buttons.If one of these buttons is selected at random, what is the probability of selecting a red button? (Express your answer as a decimal or fraction, not as a percent.)
原库参考解析
概率与条件概率进阶
The table shows the distribution of people in a certain city by age group.
If a person in this city is selected at random, which of the following is closest to the probability of selecting a person who is greater than 65 years old, given that the person is at least 18 years old?
原库参考解析
概率与条件概率进阶
Each rock in a collection of 70 rocks was classified as either igneous, metamorphic, or sedimentary, as shown in the frequency table.
If one of these rocks is selected at random, what is the probability of selecting a rock that is igneous?
原库参考解析
概率与条件概率进阶
The table summarizes members of a local organization by age and whether they live north or south of Center St. If a member of the organization is selected at random, what is the probability that the selected member is at least 45 years old?
原库参考解析
概率与条件概率挑战
The table gives the distribution of favorite core subject and grade level for 80 students.
If a student is selected at random, what is the probability of selecting a student whose favorite core subject is mathematics?
原库参考解析
概率与条件概率进阶
The table gives the distribution of favorite core subiect and grade level for 80 students.
If a student is selected at random, what is the probability of selecting a student whose favorite core subject is mathematics?
原库参考解析
概率与条件概率进阶
The table summarizes members of a local organization by age and whether they live north or south of Center St. If a member of the organization is selected at random, what is the probability that the selected member is at least 45 years old?
原库参考解析
概率与条件概率进阶
on a particular assembly line,51 out of every 100 products have a defect. A product from the assembly line will be selected at random. what is the probability of selecting a product that has a defect?
原库参考解析
概率与条件概率进阶
The table gives the distribution of favorite core subject and grade level for 80 students.
If a student is selected at random, what is the probability of selecting a student whose favorite core subject is mathematics?
原库参考解析
概率与条件概率进阶
A certain book has 250 pages, and 21 of these pages have an illustration. If one of the book's pages is selected at random, what is the probability of selecting a page with an illustration? (Express your answer as a decimal of fraction, not as a percent.)
原库参考解析
概率与条件概率进阶
A certain book has 250 pages, and 21 of these pages have an illustration. If one of the book's pages is selected at random, what is the probability of selecting a page with an illustration? (Express your answer as a decimal or fraction, not as a percent.)
原库参考解析
概率与条件概率进阶
The table summarizes members of a local organization by age and whether they live north or south of Center St. If a member of the organization is selected at random, what is the probability that the selected member is at least 45 years old?
原库参考解析
