This definition is inadequate. It is more like the definition of one's will without a definition of the "free" adjective in front of the word "will".
What is the definition of FREE? FREE from what?
I can offer a person a $1,000,000,000,000 and your definition of "free will" would fit as the person would be able to chose to take and not take the money. Similarly, I can tell a person I will put a knife in their chest, but the decision will be up to them. Again, this would be an example of your definition of a person to exercise "free will".
There are two definitions of "free will" that are commonly used that I know of:
1) Libertarian free will means that our choices are free from the determination or constraints of human nature and free from any predetermination by God. All "free will theists" hold that libertarian freedom is essential for moral responsibility, for if our choice is determined or caused by anything, including our own desires, they reason, it cannot properly be called a free choice. Libertarian freedom is, therefore, the freedom to act contrary to one's nature, predisposition and greatest desires. Responsibility, in this view, always means that one could have done otherwise.
2) God or anyone else determines any of your choices.
Without a clearer definition of "free will" I don't see this discussion going well.