1999 AMC 8 Problem 10

Attempt Problem 10 of the 1999 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1999 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

10.

A complete cycle of a traffic light takes 6060 seconds. During each cycle the light is green for 2525 seconds, yellow for 55 seconds, and red for 3030 seconds. At a randomly chosen time, what is the probability that the light will NOT be green?
14\dfrac{1}{4}
13\dfrac{1}{3}
512\dfrac{5}{12}
12\dfrac{1}{2}
712\dfrac{7}{12}
Answer: E
Concepts:geometric probabilitycomplementary probability
Small hint:
Not green means red or yellow
Big hint:
Use time not green over total cycle time
Solution:
During a given cycle, the light is not green for 30+5=3530 + 5 = 35 seconds.
Then the probability that it is not green is 3560=712. \dfrac{35}{60} = \dfrac{7}{12}.
Thus, E is the correct answer.
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