I remember reading a responsum on the issue of agnostic Jew's serving as the tenth for a minyan, but do not remember the outcome. Does anyone know the rule?
Also, do we count, as the tenth man, a tinok shenishbah and one who does not understand the prayers at all?
If it is permitted, would it be different for a lower level of chiyuve (obligation) for a minyan such as Maariv?
If it is forbidden, would it be different for a higher level of chiyuve for a minyan such as Zimun, or someone who has a chiyuve for kaddish.