AMC 12 2007b Problem 13

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?

$\mathrm {(A)} \frac{1}{63} \mathrm {(B)} \frac{1}{21} \mathrm {(C)} \frac{1}{10} \mathrm {(D)} \frac{1}{7} \mathrm {(E)} \frac{1}{3}$