Sorry, but this makes absolutely no sense, whatsoever. If one "chooses" to "believe or not," one is performing a 'work.' -indeed, the biggest 'work' of all.
You may conclude that belief (faith) is a work, but God declares that it is not a work. He says that it is a gift.Galatians 2:8-9 For by grace are you saved, through faith, and that, not of ourselves, it is the gift of God, not of works, lest any man should boast.So who ya gonna believe ?
Eph 2:8-9 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:Not of works, lest any man should boast.
The grammar here indicates that: the faith is not of yourself, it is God's gift. Works refers back to grace as the means of salvation, showing that it is not works that saves you, but grace operating through faith which God gives you, so that no man can boast or claim he saved himself or did anything to secure his salvation.
If faith were a "work", then it would not be a gift from God, but something we could do ourselves. Biblically, we can do nothing to obtain salvation, we have no qualitites in us that are salvable. It is God's Grace and Mercy shed upon us, and by that Grace and Mercy, through the faith which God Himself gives us, that we are able to believe, receive, and be justified, clothed with the righteousness of Christ. It is all of God, all God's working in us, and we have done, and can do nothing to either gain it, earn it, or deserve it.