If you are in CS/Machine Learning, you will be forced/suggested to take a few statistics/probability courses, typically up to a regression course. These are good enough to get you started and familiar with statistical concepts and methodology.
However, if you come from a typical statistics program, programming/computing courses are almost always never required. Professors in probability theory/statistics often do not have great computing skill, they might know enough to get around in R/Mathlab, and teach you the basics in these tools, but a lot of times you are left in the dark in terms learning how to code.
If your career goal is an analyst, whose job is report oriented, you can get by by knowing just enough R (SAS, Matlab etc.) scripting. As your deliverables are generally fancy LaTex pdf (or presentations). But current job market pays and values more of a "data scientist", whatever that terms mean. This type of roles typically requires solid software engineering background, and requires you to be able to work with software developers and commit to the same codebase on a regular basis. The lack of programming/computing skills of a stats majored students will be a huge minus for this type of responsibilities.