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5. You are given 3 boxes. 1 box contains a million dollars, the others is empty. If you pick correctly which box has the million dollars, you win the million dollars.
Suppose you pick Box 1. The host then opens Box 3 to show you it's empty, then he asks you if you want to change your choice to Box 2. From a probability aspect, would it matter if you changed your choice or not?

From a probability standpoint yes.
By the host eliminating 1 choice, you can choose between 2 that it might be and 1 that it isn't, therefore you get an extra 33.3 percent chance,
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6. You are in a classroom full of 20 students. Everyone has a paper. The teacher says exchange papers with everyone that is shorter than you. How many total exchanges will there be?

My guess is 0. Both people can't be shorter than another, and if you're the same height there is no exchange.