Well, let's say I have a
Suppose I have already tossed 99 times, and I got heads EVERY time. (Hey, it's possible.) Now if you were to bet on what I'd get the hundredth time, what'd you say? There are three possible answers:
a) I won't get heads again, because, well, luck has favoured me this far, but it may not favour me again.
b) I will get heads again, because, hey, I'm on a roll.
c) You refuse to bet, because the new toss is independent of the others. Or maybe just because both a) and b) seem equally convincing.
Well, we know c) is right. Problem is, why is it right? I mean, sure, independent toss and all, but isn't it even MORE improbable that I get 100 heads one after the other? Also, please don't accuse my rupee coin of being biased. It's a little sensitive these days.
So, my question to you is: give me a concrete reasoning WHY the probability on the 100th toss too is 50-50. (Maybe you don't agree it's c). Do say so. ) Double points if you can give some calculations. Triple if you can drag in Gauss. (More accurately Poisson. Actually, their curves. I mean 'distributions', dude.)
P.S. Of course you're to answer in Comments. You can also comment in comments. Also, if you have given an answer, I'll only approve the comment after I feel everyone's done the best they can. If you do find something in the comments section, it may be a spoiler.
Hint: Read my first comment below (beneath the ones by Saskia, Anne and Jayanth).