AMC8 1999

AMC8 1999 · Q10

AMC8 1999 · Q10. It mainly tests Probability (basic).

A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds, and red for 30 seconds. At a randomly chosen time, what is the probability that the light will NOT be green?

一个完整的交通灯周期需要 60 秒。每个周期灯绿灯 25 秒，黄灯 5 秒，红灯 30 秒。在随机选择的时刻，灯不是绿灯的概率是多少？

(A) $\frac{1}{4}$ $\frac{1}{4}$

(B) $\frac{1}{3}$ $\frac{1}{3}$

(D) $\frac{1}{2}$ $\frac{1}{2}$

(E) $\frac{7}{12}$ $\frac{7}{12}$

Answer

Correct choice: (E)

正确答案：（E）

Solution

\[\frac{\text{time not green}}{\text{total time}} = \frac{R + Y}{R + Y + G} = \frac{35}{60} = \boxed{\text{(E)}\ \frac{7}{12}}\] The probability of green is $\frac{25}{60} = \frac{5}{12}$, so the probability of not green is $1- \frac{5}{12} = \boxed{\text{(E)}\ \frac{7}{12}}$ .

\[\frac{\text{非绿灯时间}}{\text{总时间}} = \frac{R + Y}{R + Y + G} = \frac{35}{60} = \boxed{\text{(E)}\ \frac{7}{12}}\] 绿灯概率是 $\frac{25}{60} = \frac{5}{12}$，所以非绿灯概率是 $1- \frac{5}{12} = \boxed{\text{(E)}\ \frac{7}{12}}$。

Topics

CP.006 Probability (basic)