Statistical distribution functions are derived for the polarization of optical waves transmitted through a random medium. Excellent agreement is obtained with experiment. Our most significant result is the distribution function for the ellipticity , the ratio between the major and minor axes of the elliptically polarized scattered light. This has a maximum at =0 and vanishes for =1, indicating that linear polarization is the most probable state and that circular polarization has vanishing probability. The averaged ellipticity is found to be =1-ln2=0.307.