3 ms·

Sorry but right after you finish the basic probability coverage it stops making sense. -> In the case of the two envelopes the problem comes from the fact that

• jamii 13y ago
  Well, with the distribution I gave it could be $2 (with probability 1/2), or $4 (with probability 1/4), or $8 (with probability 1/8) etc. That distribution doesn't have a maximum. For a simpler example, imagine tossing a coin and counting the number of tosses it takes you to get a head. There is no limit on the number of tosses it might take, it just gets less and less likely as the numbers get bigger. We could get any positive integer and there are an infinite number of integers. Similarly, the envelope problem has an infinite number of possibilities because there is no maximum amount that could be in the envelope. The article doesn't specify the exact odds of any given amount showing up in the envelope so I gave some specific odds that demonstrate the problem. Probability theory still works when you have an infinite number of possibilities but it has a few subtleties that aren't commonly taught until undergrad. One of those is that the expected/average value of a random variable doesn't always exist so you have to be careful when reasoning informally.