  Chaotic orbits of mushroom billiards display intermittent behaviors. We
investigate statistical properties of this system by constructing an infinite
partition on the chaotic part of a Poincar\'e surface which illustrates details
of chaotic dynamics. Each piece of the infinite partition has an unique escape
time from the half disk region, and from this result it is shown that, for
fixed values of the system parameters, the escape time distribution obeys power
law $1/t_{\rm esc}^3$.
