2007 AMC 12B Problem 13
Below is the professionally curated solution for Problem 13 of the 2007 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 12B solutions, or check the answer key.
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Difficulty rating: 1410
13.
A traffic light runs repeatedly through the following cycle: green for seconds, then yellow for seconds, and then red for 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?
Solution:
The cycle length is seconds, with three color changes per cycle.
Leah sees a change exactly when her three-second interval starts within the seconds before a switch. That gives favorable seconds out of a probability of
Thus, the correct answer is D.
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