Three candidate students (A, B, C) were signed up for a probability competition. The principal recommends one of three students at random (i.e. with the same probability). Then, the principal informs the teacher which student was chosen, and requests that the name be kept secret for a week. The next day, A tries to get the teacher to tell them who had been selected. The teacher refuses to tell. Then, A asks which of B or C will be not selected. The teacher thinks for a while, then tells A that B will not be selected. Does this information increases A's chance of being selected? That is, compare the probability of A being selected and the probability of A being selected given that the teacher says B is not selected. Assume that the teacher does not lie. (Hint: Let A, B, and C be the events that A, B, and C is selected, respectively. Let T be the event that the teacher says B is not selected. What is P(T)?)