  We study the survival probability time distribution (SPTD) in dielectric
cavities. In a circular dielectric cavity the SPTD has an algebraic long time
behavior, $\sim t^{-2}$ in both TM and TE cases, but shows different short time
behaviors due to the existence of the Brewster angle in TE case where the short
time behavior is exponential. The SPTD for a stadium-shaped cavity decays
exponentially, and the exponent shows a relation of $\gamma \sim n^{-2}$, $n$
is the refractive index, and the proportional coefficient is obtained from a
simple model of the steady probability distribution. We also discuss about the
SPTD for a quadrupolar deformed cavity and show that the long time behavior can
be algebraic or exponential depending on the location of islands.
