AS Mathematics Unit 5 June 2019 Question Paper Breakdown | AS数学单元5 2019年6月试卷题型解析

📚 AS Mathematics Unit 5 June 2019 Question Paper Breakdown | AS数学单元5 2019年6月试卷题型解析

The June 2019 AS Mathematics Unit 5 paper (commonly Statistics 1 for the Edexcel IAL specification) covers a wide range of statistical topics. In this article, we break down the key question types and provide model approaches to help you master the exam.

2019年6月AS数学单元5试卷（通常为爱德思IAL统计学1）涵盖了一系列统计主题。本文将解析关键题型并提供解题思路，助你掌握考试要点。

1. Probability and Venn Diagrams | 概率与维恩图

In Q1 of the June 2019 paper, you are often given probabilities for events A and B and asked to complete a Venn diagram. For instance, P(A) = 0.35, P(B) = 0.45 and P(A ∪ B) = 0.6.

2019年6月试卷的第1题通常会给出事件A和B的概率，并要求完成维恩图。例如，P(A) = 0.35, P(B) = 0.45, P(A ∪ B) = 0.6。

Using the addition rule, you find P(A ∩ B) = P(A) + P(B) − P(A ∪ B) = 0.35 + 0.45 − 0.6 = 0.2.

利用加法公式，可得 P(A ∩ B) = P(A) + P(B) − P(A ∪ B) = 0.35 + 0.45 − 0.6 = 0.2。

You then fill in the intersection and the remaining exclusive probabilities. A typical follow‑up asks for P(A ∪ B’) or a conditional probability like P(A | B).

然后填写交集及互斥概率。常见的后续问题是求 P(A ∪ B’) 或条件概率如 P(A | B)。

Remember the formula:

记住公式：

P(A | B) = P(A ∩ B) / P(B)

In this case, P(A | B) = 0.2 / 0.45 = 4/9 ≈ 0.444.

在此例中，P(A | B) = 0.2 / 0.45 = 4/9 ≈ 0.444。

Always check whether events are independent by verifying P(A ∩ B) = P(A) × P(B). If not equal, they are not independent.

务必检验事件是否独立，验证 P(A ∩ B) 是否等于 P(A) × P(B)。若不相等，则不独立。

2. Tree Diagrams and Conditional Probability | 树状图与条件概率

Whether it is Q2 or part of a longer question, tree diagrams appear regularly. The June 2019 paper might provide two stages of an experiment, e.g., drawing counters from a bag without replacement.

无论是作为第2题还是大题的一部分，树状图经常出现。2019年6月试卷可能给出两阶段试验，例如不放回地从袋中抽取筹码。

Label branches with probabilities, making sure the probabilities on the second set of branches sum to 1. Use the multiplication rule along branches.

在分支上标注概率，确保第二层分支概率之和为1。沿分支使用乘法法则。

To find ‘at least one’ type probabilities, it is often easier to use the complement: P(at least one) = 1 − P(n

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