Monty Hall With Envelopes

Probability · Easy · Free problem
You are given three envelopes. One contains $\
$ and the other two are empty. You pick one envelope at random but do not open it. The interviewer, who knows where the money is, opens one of the remaining two envelopes and shows you that it is empty. You now have a choice: stick with your original envelope, or switch to the other unopened envelope. 1. What strategy maximizes your probability of winning the $\ $? 2. What is the probability of winning under each strategy? **Follow-up:** Now suppose the interviewer does **not** know where the money is. They open one of the remaining two envelopes at random, and it happens to be empty. Should you still switch? What is the probability of winning if you switch vs. stay?

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