[Easy E]

So, let me see if I have this straight:

In Monty Hall, your pick has a 2/3 chance to be wrong. When Monty reveals wrong answer (door C) in the remaining choices, KNOWING that you picked door A, the chance that you should switch is 67%, not 50%

In the test, your original pick also has a 2/3 chance of being wrong. The instructor reveals wrong answer (#C) in the remaining choices, WITHOUT knowing that you picked #A. Now, your chance of being wrong with #A is 50%, not 67%.

And the difference is because, not knowing what you picked, the instructor could have told you that #A was the wrong answer, where Monty Hall eliminated revealing your door A as a goat?

Someone please get through my little ole brain how the dependency is gone in the second situation, given that the instructor did NOT pick #A as the answer to reveal, even though they could? I understand that the instructor's relevation gives #A and #B a 50/50 chance... but why did that change YOUR odds of #A being wrong originally, since you did NOT have any more info than in Monty Hall- except for that the instructor's choice was random and Monty's was not?

Am I putting too much weight on the wording that says you picked #A and the instructor did not, even though s/he could have?

I hope there's a mathematical principle behind this, because the verbiage is giving me a headache...