2007 AMC 12B 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}\qquad \mathrm {(B)} \frac{1}{21}\qquad \mathrm {(C)} \frac{1}{10}\qquad \mathrm {(D)} \frac{1}{7}\qquad \mathrm {(E)} \frac{1}{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.