On a game show, elena is given the choice of three doors: behind one door is the grand prize; behind the others, consolation prizes. she picks door a, and the host, who knows what is behind each door, opens door b, revealing a consolation prize. the host then offers elena the opportunity to change her selection to door c. what should she do?

a. she should not accept because the probability of door a being the grand prize increased.
b. she should accept because the probability of door c being the grand prize increased.
c. she could either accept or not accept because now the probabilities of both doors are equal.
d. she could either accept or not accept because the probabilities of the three doors were equal from the beginning.