Pondering Probability

goatOn Let’s Make a Deal game show, one door out of three has a new car, the other two have goats.  You pick door #1, and the host (knowing which door has the car) shows you that door #3 has a goat behind it.  you are down to two doors, and the host asks, “OK, do you want to switch doors now?”  If you switch to door #2, you now have a higher probability of winning the car.  Can you explain why?

This is how I understand it…..

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