Crazy Math Problem
In Probability today, the professor was talking about the Monty Hall problem, a pretty counterintuitive probability problem that I learned about in Freshman year, back in Andy Barto's discrete math course. Then he told us about a similar problem, and it fucking blew my mind.
Here is the problem: you are presented with two envelopes, each of which has a real number in it; the two numbers are different. You are allowed to look inside either of the envelopes, and then have to either choose that envelope or the other one. The question is, is it possible to come up with a strategy that will let you choose the envelope with the bigger number more than half the time? You know nothing about where the numbers in the envelopes came from, e.g. whether they are drawn from some kind of probability distribution.
I'm going to write the solution to this question as a comment to this post, but I recommend waiting a day or so before reading it to think about the problem during some spare moments.
Here is the problem: you are presented with two envelopes, each of which has a real number in it; the two numbers are different. You are allowed to look inside either of the envelopes, and then have to either choose that envelope or the other one. The question is, is it possible to come up with a strategy that will let you choose the envelope with the bigger number more than half the time? You know nothing about where the numbers in the envelopes came from, e.g. whether they are drawn from some kind of probability distribution.
I'm going to write the solution to this question as a comment to this post, but I recommend waiting a day or so before reading it to think about the problem during some spare moments.