On a game show, Elena is given the choice of three doors: Behind one door is the Grand Prize; behind the others, consolation pri
zes. 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?
From the very beginning, each door had a 1/3 probability chance to be holding the grand prize. And the fact that she saw the consolation prize behind one of them does not change this probability. From the beginning, all doors had equal chances.
Based on this, the answer to your question would be: She could either accept or not accept the host's offer <span>because the probabilities of the three doors were equal from the beginning.</span>
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