Thanks for the response! I've been told that probability theorists are generally scattered in different departments (applied math, statistics, operations research, engineering, etc.), but are mostly found in math departments.
My program requires the probability-statistics sequence, as well as a few other applied statistics courses, so I will definitely be taking those courses. Thanks for the PDEs suggestion.
I've also been told that Numerical Analysis is probably the least important of the above sequences, but wouldn't it be important for applied math applications?