I am pasting the below from Wikipedia:
I don’t get how people actually manage to convince themselves the answer is 2/3.
The question concerns whether it is to your advantage to switch from one box to another. That situation only involves two boxes, one with a goat in it and one without. A third box is irrelevant.
“Yeah well before there were three at the beginning and your initial choice had a probability of 1/3 which was 2/3 wrong; those other two boxes you did not pick had a total probability of 2/3, so it is in your advantage to choose that one”
Only if you think human probability somehow magically alters future situations in order to preserve the probability of now non existing situations.
“We are confident that the new cell phone design will be well received. Statistics show that blah blah blah”
“Makes sense. What are your sources?”
“A, B, C, D and E”
“What about previous statistics? Did you take those into account?”
“I’m sorry, what previous statistics?”
“You know, past chances of making a huge product on new cell phones”
“Oh yes of course we took into account the iphone, blackberries, and also an upcoming release that is combination of touch screen technology and–”
“Yes yes, cell phones that are in the market now, I understand that.”
“Well… what else is there?”
“All statistics concerning all market value for past cell phone releases”
“All of them?”
“All of them”
“All statistics concerning probabilities of success for cell phones nobody can even buy, in markets that don’t even apply to the one we’re now in?”
“Absolutely, all of them.”
“Well… if you take the probability of all the cell phones being successful in their respective situations I guess that gives a total chance of, I dunno, at least 10/1…”
“What does that mean?”
“It means 10 x absolute certainty that the sum of the past chances of past cell phones in their past markets would be a profit”
“That’s incredible! I wish I was in this business earlier, HAHA!”
“Well, I mean those statistics really mean anything… I am actually just calling success ‘1/1’ and then, for the real past money-makers, giving them values like ‘3/1’, because they made three times more than what would have been a success… you see I am judging their past probability based off what happened after the fact”
“But it’s statistics, right?”
“Well… I mean, I guess…”
“Great work! Is that all?”
“All what? I mean, I didn’t include most failures because I just don’t remember them.”
“Oh no no, I don’t care about cell phones, I care about the past statistics concerning them”
“Oh, yeah, that’s all”
“So how does this affect our chances?”
“Ohh… well since we want to make a profit, and our cell phone is not any of those cell phones, I guess our chances are 10 times absolute failure”
“THEN WHY ARE WE WORKING ON THEM?!”
“Sir I think you’ve mis–”
“STOP WASTING OUR MONEY!”
“But SIR, our current numbers tell us that we are very likely to succeed here! Not only would we lose an opportunity but all the money that we have already put into this would b–”
“What are our losses?”
“Well… let me see… about 8 times that which we needed to make in order to make a decent enough profit to label the project a success.”
“8? Are you sure it’s not 10?”
“Yes I’m sure”
“Which is why you’re fired! I need someone who knows his statistics”