Christmas Contest - Team Round - Problem 10

Tommy and Frances are playing a game with darts and a toy clock. Frances spins the two hands on the clock, and the hands land at a random angle from the center of the circle.

Tommy, blindfolded, throws a dart at the clock. If the dart lands at a random location on the clock, let the probability that the dart is in the smaller angle formed by the two hands be \tfrac{a}{b} where \gcd(a,b)=1. Find 100a+b.