We test the hypothesis that radio galaxies are a random subset of otherwise normal elliptical galaxies. Starting with the observed optical luminosity functions for elliptical galaxies, we show that the probability of an elliptical forming a radio source is a continuous, increasing function of optical luminosity, proportional to L2+/-0.4. With this probability function and the luminosity function of normal elliptical galaxies as input to Monte Carlo simulations, we reproduce the observed distribution of radio galaxies in the radio-optical luminosity plane. Our results show that radio galaxies are a luminosity-biased but otherwise random sample of elliptical galaxies. This unified view of radio-loud and radio-quiet ellipticals also explains the well-known difference of ~0.5 mag in average optical luminosity between FR I and FR II radio galaxies as a simple selection effect. Specifically, FR II galaxies appear preferentially in smaller galaxies because both radio and optical luminosity functions are steep, so there is a negligible probability of observing a powerful radio source associated with a bright galaxy; no intrinsic physical differences between FR I and FR II host galaxies are required.