The role of probability in solving the Monty Hall problem

[ErGingerbreadMandude]

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Since you have a 50-50 chance of having chosen a goat initially, [...]

LOL... How do you figure that? Since initially you were choosing from 3 doors, behind which there are 2 goats and 1 car - therefore you have a 66-33 chance of having initially chosen the goat. It does not matter, that one of the goat-doors was opened afterwards - your chances of having picked a goat are the same.

Because we know that there is a goat behind one of the doors after the host shows it to us. Then we have a 50-50 chance of having chosen a goat initially.