I am going to respectfully disagree with the information that has been provided.
The purpose of naming a beneficiary is so that money can be transferred upon the death of the owner without a will being probated. If mom has that much money, she may need to speak with an estate planner who can assist with minimizing inheritance taxes, as well as structuring her deposits to increase FDIC coverage.
However, if her only goal is to avoid probate, any assets with a named beneficiary do not have to be probated.
Ohiobar.org Q & A on probate