If the world were that simple But in real life it does matter.
Because of the wording of the OP: "Each one of them upon being asked the first( yes or no) question ,will randomly choose to be a truth teller or a liar. And as he did he will be fixed to that persona and will not change it( i.e.If he tells the truth,will always tell the truth, if he lied,will always lie)." I am not sure that my previous trick could or could not work this time for the first question. It depends on when he decides: before/during the question.
However if the person knows before answering if he is forever going to be a truth-teller or forever going to be a liar then with some rewording: