We've all heard that the SWO boards are looking for technical majors, but hopefully this post (copied from usnavyocs.com) will give you hope:
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Heather,
The Navy needs us Arts and Crafts majors also. I am finishing up my degree in English and American Literature with a minor in Philosophy this semester and I have a Surface Warfare Slot. My situation is a little different than yours based on the facts that I got into BDCP prior to 9/11 and have 8 1/2 years of prior service in the Marine Corps, so these things may have been a factor in my selection. I would encourage you to go for it!
Jamie
BDCP, SWO
(Sgt, USMC 91-99)
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Give it a shot. What's the worse that could happen?