Hehe, Last time i dropeed it like that because it was very apparent that arguing the point was useless. You cannot convince some people the earth is round. I have taken plenty of math classes in my time. I suggest waiting to hear back from the stetician before talking trash like that.
My point is that you are resetting the odds each time. If you started with 60 envelopes, with 20 correct ones and 40 incorrect, he would have a 2.4% chance of getting all 20 correct, if you do sets of 3 where the previous envelopes are removed each time and it is reset to 1 correct, 2 incorrect, the odds will always be 1/3, so in a total of 20 tires, that would be 20/60, or 33%. But like I said, if you start with all 60, 20 being correct, each choice would reduce the odds, meaning, the first choice he would have 33% chance (20 correct cards, 40 incorrect), 2nd choice he would have a 32.2% (19 correct cards, 40 incorrect), keep going until the last one, which he would have a 2.4% chance of getting the correct one (1 correct card, 40 incorrect), which would satisfy the odds requerment.