维恩图与结果计数
Venn Diagrams and Counting Outcomes
构建并解读包含两个或三个集合的维恩图，用它们来整理和计数结果；运用系统列举和乘法计数原理，列举出组合事件的所有可能结果。
Construct and interpret Venn diagrams with two or three sets to organise and count outcomes; use systematic listing and the product rule for counting to enumerate all possible outcomes of combined events
学习证据 / Evidence
- 画一个双圆维恩图，将30名学生按喜欢足球、喜欢板球或两者都喜欢进行分类。
- 在维恩图上用阴影标出交集 A ∩ B 和并集 A ∪ B，并解释每个区域代表什么。
- 使用一张已完成的维恩图来计算 P(A)、P(B)、P(A ∩ B) 和 P(A ∪ B)。
- Draw a two-circle Venn diagram to sort 30 students by whether they like football, like cricket, or like both
- Shade the intersection A ∩ B and the union A ∪ B on a Venn diagram and explain what each region represents
- Use a completed Venn diagram to calculate P(A), P(B), P(A ∩ B), and P(A ∪ B)
评估问题 / Assessment
如果{{name}}调查一个班级的学生都参加了哪些体育运动，并画出一张维恩图来展示结果，那么能否用这张图找出同时参加两项运动的学生人数，并计算随机抽到其中一名学生的概率？
If {{name}} surveys a class about which sports they play and draws a Venn diagram to show the results, can they use it to find out how many students play both sports — and calculate the probability of picking one of those students at random?