Problem restated: You are participating as a contestant in a 1960's game show the host informs you that behind one of the three large doors in front of you there is a grand prize of a new car, boat, 787 Dreamliner etcetera and behind the other two doors are goats with their weird horizontal pupils. He then asks you to pick which door you think has the grand prize behind it. Afterwards the host then opens another door revealing a goat. It is important to note that the host knew that the door he opened had a goat behind it before hand. Finally the Host asks you if you would like to change your selection to the other unopened door. what is your response? Explain in a few short sentences and using probabilities.