I read this story in a book called ‘The Black Hole War’ by Leonard Susskind. It just goes on to demonstrate the fallacy of probabilistic statements. Here’s the story then –
Student: Hi Prof. I’ve got a problem. I decided to do a probability experiment- you know, coin flipping and check some of the stuff you taught us. But it didn’t work.
Prof: Well I’m glad to hear you are interested. What did you do?
Student: I flipped this coin 1000 times. You remember you taught us that the probability of flipping heads is one-half. I figured that it meant if I flip the coin 1000 times I should get 500 heads. But I got 513. What’s wrong?
Prof: Yeah but you forgot about the margin of error. If you flip a certain number of times then the margin of error is about the square root of the no of flips. For 1000 flips the margin of error is about 30. So you were within the margin of error.
Student: Ah, now I get it. Every time I flip 1000 times I will always get something between 470 and 530 heads. Every single time! Wow, now that’s a fact I can count on.
Prof: No,no ! What it means is that you will probably get between 470 and 530.
Student: You mean I could get 200 heads ? Or 850 heads? Or even all heads?
Prof: Probably not
Student: Maybe the problem is that I did not make enough flips. Should I go home and try 10,000 flips? Will it work better?
Student: Aw come on Prof tell me something I can trust. You keep telling me what probably means by giving me more probablies. Tell me what probability means without using the world probably
Prof: Hmm. Well how about this: It means that I would be surprised if the answer were outside the margin of error.
Student: My God! You mean all that stuff you taught us about Statistical and Quantum Mechanics and mathematical probability: all it means is that you’d personally be surprised if it didn’t work ?
Prof: Well, uh …….
If I were to flip a coin a million times I’d be damn sure I wasn’t going to get all heads. I’m not a betting man but I’d be so sure that I’d bet my life or my soul. I’m absolutely certain the Laws Of Large Numbers- probability theory- will work and protect me. All of science is based on it. But I can’t prove it and I don’t know why it works. That may be the reason Einstein said God Does Not Play Dice. It probably is.