Re: typo
I think you'll find that as the noun (investigation) starts with a vowel that the statement correct, private in this case being an adjective.
However, if the adjective and noun had been joined by a hyphen then you would have been correct.
The anomoly in the very first sentence is explained (IIRC) that it is not permissable to start a sentence with An.
Biting the hand that feeds IT
