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?
Pick one
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
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