Question

一个交通灯不断重复以下周期：绿灯 $30$ 秒，然后黄灯 $3$ 秒，然后红灯 $30$ 秒。Leah 随机选择一个三秒钟的时间段观察交通灯。在她观察期间灯变色的概率是多少？

A traffic light runs repeatedly through the following cycle: green for $30$ seconds, then yellow for $3$ seconds, and then red for $30$ seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching?

$\dfrac{1}{63}$

$\dfrac{1}{21}$

$\dfrac{1}{10}$

$\dfrac{1}{7}$

$\dfrac{1}{3}$

答案：D

知识点：几何概率

难度评级：1410

解答：

周期长为 $30+3+30=63$ 秒，每周期有三次变色。

Leah 看到变色当且仅当她的三秒观察区间在某次变色前的 $3$ 秒内开始。共有 $3\cdot3=9$ 秒的有利开始时间，在 $63$ 秒周期中概率为 $\dfrac{9}{63}=\dfrac17.$

所以正确答案是 D。

The cycle length is $30+3+30=63$ seconds, with three color changes per cycle.

Leah sees a change exactly when her three-second interval starts within the $3$ seconds before a switch. That gives $3\cdot3=9$ favorable seconds out of $63,$ a probability of $\dfrac{9}{63}=\dfrac17.$

Thus, the correct answer is D.

2007 AMC 12B 第 13 题

答案：D

难度评级：1410

解答：

其他年份的第 13 题