is dual majoring a worthwhile endeavor?

Yes, they probably will have a lot of common coursework. As a Biology major, I found that my courses overlapped with students in many other branches of science. On one hand, this will be helpful because you will be able to take courses that will count for both majors, on the other hand, you may find that it isn't exactly beneficial to achieve both of these majors. I would highly recommend you sit down with a guidance counselor and discuss what your career goals are. This will help you determine if dual majoring is beneficial for you.