京都大学 情報学研究科 知能情報学専攻 2019年2月実施 基礎科目 F2-2

标签：

• Kyoto-University
• Proportion-and-Base-Rate

Author

祭音Myyura (co-authored with GPT 5.6 SOL)

Description

Minister X claims that his policies for preventing motorbike accidents caused by young drivers are successful: the number of young drivers causing motorbike accidents has halved. His political opponent, Mr. Y, argues on the other hand that the proportion of motorbike accidents that are caused by young drivers has increased from 20% to 40%.

(1) Explain briefly why Minister X's and Mr. Y's assertions do not contradict with each other.

(2) $A_0$ is the initial total number of accidents (with both young and old drivers), and $A_1$ is the total number of accidents after Minister X's policies. Express $A_1$ in terms of $A_0$.

题目描述

部长 X 声称其预防年轻驾驶者摩托车事故的政策有效，因为年轻驾驶者造成的事故数减少了一半。其政治对手 Y 则称，年轻驾驶者造成的事故占全部摩托车事故的比例从 $20\%$ 上升到 $40\%$。

1. 简要说明两种说法为何并不矛盾。
2. 设政策前的总事故数（年轻与年长驾驶者合计）为 $A_0$，政策后的总事故数为 $A_1$。用 $A_0$ 表示 $A_1$。

Kai

Q.2.1

The assertions concern different quantities. Minister X refers to the absolute number of accidents caused by young drivers, whereas Mr. Y refers to that number as a proportion of all accidents. The absolute number can fall while its proportion rises if the total number of accidents falls even faster.

Q.2.2

Initially, young drivers caused

$$0.20A_0$$

accidents. After this number is halved, it is $0.10A_0$. Since it is also $40\%$ of the new total,

$$0.40A_1=0.10A_0.$$

Therefore

$$\boxed{A_1=\frac14A_0}.$$

Indeed, young-driver accidents decrease from $0.20A_0$ to $0.10A_0$, while the total decreases from $A_0$ to $0.25A_0$, so the proportion rises from $20\%$ to $40\%$ without contradiction.