A traffic light runs repeatedly through the following cycle: green for \(30\) seconds, then yellow for \(3\) seconds, and then red for \(30\) 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? Provide your answer in the form \(\frac{k}{m}\) where the fraction is in simplest form, and find the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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