You pick one of three doors hiding a car, the host reveals a goat behind another door, and offers you a switch. Should you switch?
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You choose one of three doors, behind one of which is a car and behind the other two are goats. The host, who knows what is behind each door, opens one of the remaining doors to reveal a goat, then asks if you want to switch your choice. Should you switch?
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You choose one of three doors, behind one of which is a car and behind the other two are goats. The host, who knows what is behind each door, opens one of the remaining doors to reveal a goat, then asks if you want to switch your choice. Should you switch?
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Yes, switching doubles your odds of winning the car, from 1-in-3 to 2-in-3, because the host's reveal provides new information that shifts probability toward the unchosen, unopened door.
