2007 AMC 12B Problems/Problem 13
Problem 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 traffic light runs through a second cycle.
Letting reference the moment it turns green, the light changes at three different times: , , and
This means that the light will change if the beginning of Leah's interval lies in , or
This gives a total of seconds out of
See Also
2007 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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