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The trick is that the host does not pick a door to open at random... If they did there would be a 1/3 probability they opened your door. If they didn't open you
by rfrey 5y ago
The trick is that the host does not pick a door to open at random... If they did there would be a 1/3 probability they opened your door. If they didn't open yours under that circumstance, there would be a 50/50 chance you already picked the good door.
But it's not random... Monty will never open the door you chose. That's what messes up the intuitive probabilities.
- billforsternz 5y agoNot only will he not open the door you choose, he won't open the door in front of the car either. I think that's the key point that confuses people. He knows where the car is and he always exposes a goat instead.