Please tell if my statement is correct.

Yes, 'the' (the definite article) is required because the noun is a specific thing (the presence of mind of a [unique, single] person). You would omit it for a noun denoting a general category or abstract thing, e.g. "How would this question determine presence of mind in old people?".

Main rule:
The definite article "the" (invariable in form) designates a person, place, or event which has been specified or defined by the speaker:

Here's the book I bought.
The cat is on the roof.
He said he would bring the money.

Omission of the definite article
No article is necessary in the following cases:

Before abstract nouns or nouns representing general categories. It is often omitted after verbs expressing opinions or preferences:
Truth is the highest good.
I don't like animals.
Cats are nicer than dogs.
Time flies.
She likes coffee, but she hates tea.

Before days of the week and dates:
On Tuesdays museums are closed.
On Saturdays I sleep in.
I was born on June 16, 1980.

Before names of countries, states, cities, and regions:
France is seventeen times smaller than the United States.
California is larger than Brittany.

Exception: Some names actually include the definite article, such as The Hague, the United States (of America)

Before titles or nouns indicating professions:
President Mitterrand completed two terms.
We saw Professor Miller at the restaurant.
She met with Doctor Schmidt.

Thanks for the reply.

But isn't 'a person' indefinite? A person can be any person, how is it a unique person?

A person, real or imaginary, is one person, and therefore definite.

The noun covered by the definite article 'the' is 'presence,' not 'person'. Hope that helps.