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Suppose that a random real number x has been chosen according to some distribution and you...

Suppose that a random real number x has been chosen according to some distribution and you have two sealed envelopes in front of you. One contains the number x and the other contains the number 2x. (a) If you need to guess which of the envelopes contain the number x, what would be your probability of guessing correctly? (b) Now suppose that you are allowed to pick one envelope and look at the number inside of it before you make your decision. Can you come up with a strategy that gives you a better success rate than the one in part (a)?

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Answer #1

a)If I need to guess which of the envelopes contain the number x, probability of guessing correctly=

b) Now suppose that I am allowed to pick one envelope and look at the number inside of it before I make my decision then if the number in the envelope is the same number I need to guess then I will select the same envelope else if the number in the envelope is not the same number I need to guess then I will select the other envelope.This strategy gives us a better success rate than part (a).

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