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The solution?

8 Name: Anonymous 2021-04-14 15:54
>>1
Think of it this way, since the host will always pick a goat door whether you picked a goat door or not, the three possible scenarios after he reveals the goat door are:
1. You picked a goat door, there is a winning door unrevealed, and the host reveals the second goat door
2. You picked a goat door, there is a winning door unrevealed, and the host reveals the second goat door
3. You picked the winning door, there is a goat door unrevealed, and the host reveals the second goat door
In the first two scenarios, switching your pick will cause you to win and in the last scenario switching will cause you to lose. Since this is an exhaustive list of all possibilities, the probability of switching leading to a win goes to 0.66 repeating, up from 0.33 repeating to pick the correct door originally. If there are only two doors, the original probability is 0.50. Idk how you would apply the host opening the goat door here - if he opens it and gives you an opportunity to switch then there is no need to apply probabilities - just pick the other door

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