JogaBonito1502
Guru
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The only way your choice will not affect the host's choice is if you picked the right door, as then he can arbitrarily pick the other door and no matter what it will be empty. However, if you picked the wrong door, then your choice affects the host's choice because he cannot pick a door at random since then there is a probability that he will eliminate the door with the prize. When you extend this to n doors and let n go to infinity (a general case), then the probability that you picked the right door is ~0 and therefore the probability that the host would eliminate the correct door at random is ~1. This makes the events dependent.