Section 162(a) provides a deduction for “all the ordinary and necessary expenses paid or incurred during the taxable year in carrying on any trade or business.” The expense needs to be an ordinary and necessary expense - - meaning customary for that type of business. In the corporate field, an MBA is customary.
If you were a director prior to and during your entering the MBA program, then you meet the "carrying on" a "trade or business." Ordinarily, tuition is not deductible, for example, if you were a full-time student obtaining a degree to get employment. It seems that you were obtaining a degree to enhance a business you were already working in.
Treas. Reg. Section 1.162-5(a) provides that a taxpayer may deduct educational expenses as "ordinary and necessary" business expenses if the education maintains or improves skills required by the individual in his or her employment or other trade or business.
I assume this program did this for you as a director.
The above said, you should qualify for the deduction.
Likelihood of being audited: That's very difficult to predict. I would have to know all claims made on your return to assess whether there's a high likelihood of being audited. If you are, you should qualify for the deduction, so the audit risk would not be from the expense, though it could be from another deduction or item on your return.
Hope this helps.