Carlson, Christensen, Harris, Jones, Rodriguez. Among our results, we prove that the probability of obtaining a parking function from a preference vector of length $n$ is independent of the probability parameter $p$. Also, given that the preference vector is a parking function, we examine its properties and discuss the effect of the probability parameter $p$. Of particular interest is the case where $p=1/2$. In this case, we see a sharp change in some parking stats. We also present results for some interesting combinations of parking protocols. In particular, we provide a combinatorial interpretation of the sequences described in OEIS A220884 as the expected number of preferred sequences with specific properties relevant to the parking lot in use. This resolves an open Novelli and Thibon issue raised in 2020 (arXiv:1209.5959). Finally, we link our results to other weighted phenomena in combinatorics to provide further directions for research.
