Carolyn, you can't delete a profile here. The solution is to merge duplicate profiles. It does not matter which one is correct or not correct - the merge will result in the lower profile number of the two, provided the LNAB's (Last Name At Birth) are the same for both. You will be able to select which data (for each data item) is preserved when you complete the merge.
To get started, scroll to the bottom of one of the profiles and click the "initiate a merge" link. Post back here if you have any questions about doing it.