It is possible for a wizard to be chosen by two wands, this makes me wonder if the reverse is true. Can two or more persons having similar qualities be CHOSEN by a single wand? Moreover, is it necessary that a wizard would be chosen by a wand at all? What if the wandmaker hasn't created that particular wand by that time that would choose him.
Update:
If the wandmaker makes a wand specifically for a child, how can he be sure that the wand would choose him/her at all. At such a young age, how can a wandmaker make an idea about the child's specific qualities and temperament?
