Completeness of the Gaia-verse V: Astrometry and Radial Velocity sample selection functions in Gaia EDR3

We risk reaching false scientific conclusions if we test our physical theories against subsets of the Gaia catalogue without correcting for the biased process by which stars make it into our sample. In this paper we produce selection functions for three Gaia science samples to enable the community to correct for this bias. We estimate the probability that a source in Gaia EDR3 will have i) a reported parallax and proper motion, ii) an astrometric renormalised unit weight error below 1.4, or iii) a reported radial velocity. These selection functions are estimated as a function of $G$-band apparent magnitude and position on the sky, with the latter two also being dependent on $G-G_\mathrm{RP}$ colour. The inferred selection functions have a non-trivial dependence on these observable parameters, demonstrating the importance of empirically estimating selection functions. We also produce a simple estimate for the selection function of the full Gaia EDR3 source catalogue to be used with the subset selection functions. We make all of our selection functions easily accessible through the GitHub repository \textsc{selectionfunctions}.