4 ms·
Unless you picked 2x to start with, in which case the other envelope does contain half of what you chose... i.e. there are two envelopes, x and 2x, and you cho
by Osmium 13y ago
Unless you picked 2x to start with, in which case the other envelope does contain half of what you chose...
i.e. there are two envelopes, x and 2x, and you choose one. There is a 50% chance that the envelope you didn't choose is half the value of the one you picked (you pick 2x, and the other is x), or there's a 50% chance the envelope you didn't choose is twice the value of the one you picked (you pick x, and the other is 2x). I think it's misleading to introduce this "third" quantity of 0.5x... but perhaps I'm missing something subtle, in which case I'd be happy to be corrected!
- dools 13y agoI think it's misleading to introduce this "third" quantity of 0.5x Yes, it is misleading, that's my point :) Put it another way: you have two quantities in two envelopes, A and B. If you choose B, what is the probability that the other envelope contains a 3rd quantity, C? The probably of that is zero, because C was not present in the initial two envelopes. Still another way of putting it: I will place $10 in an envelope, and $20 in another envelope, then ask you to choose one. What are the chances that the other envelope contains $40? The chance of that is zero, because the only two amounts present at the start of the trick were $10 and $20.