I can’t help with estimating odds, but for majors (in addition to @merc81’s data science suggestion) I wanted to note that for an interest in STS, you probably know there’s a significant overlap with Sociology departments, though you can actually find STS folks in a number of different areas. You might take a look at an interdisciplinary STS institute (like Berkeley’s CSTMS) and see what departments their professors are in and see if any of those academic areas sound appealing to you.
You might have trouble finding many STS majors, as it often seems to be a minor (like at Rice (here), or Georgetown (here)), or an “additional major” (like at Carnegie Mellon (here)). You can take a look at College Navigator, though. Here’s a list of schools that have some sort of STS discipline, based in City/Suburban/Town environments: College Navigator - Search Results. You can fiddle with the filters on the left side of the screen to adjust the results (like % of Applicants Admitted to find more accessible schools).