Mathematical Conundrum or Not? Number Six Anyone remember the discussion of the coin flip?
You flip a coin, before it lands it has a 50/50 chance for H or T. After it lands what is its chance for H or T?
Remember that?
You flip a coin, it has a 50/50 chance of being H or T, it lands on H that event is over and done with; physically the coin cannot be T. However, you don't look at it, so you guess that it could be H or T, and you give each a 50/50 chance. That is your guess and the probability applies to your guess. You guess can never change the actual value on the coin.
You randomly selected , and the chance of selecting that value is , which is unknown, but after it is selected what is its chance of being selected? 0, as the event is already decided. The contents of the envelopes cannot change no matter what you guess at, that event is over and done with and both envelopes have been filled.
By the time you are looking at your 10 bucks the contents of both envelopes has already been decided and is set in stone. Since the contents of both envelopes is determined at the same time by the same method then the probability of both must always be equal. If your model does not conform to this truth then you are wrong.