Probability

As I keep spending more n more time on noise characteristics and its modelling, I cudn't help but wonder at how efficiently it works out in practice, not withstanding our incomplete understanding of the physical world..

Probability!! when I first studied it in school, I never imagined it wud be so useful in the practical real world.. guess it comes from my incomplete understanding of the concept. The first example everyone is told in probability class is certainly misleading.. atleast to me.. when you toss a coin, we are told it's equally probable for the outcome to be either heads or tails.. and intuitively, though it seemed true and trivial.. I had a nagging sense of doubt that if the conditions were all exactly the same, there is no reason for the outcome to be different in different experiments!

And isn't it true?? and does this not apply to any event? Why would/should there be any scope for randomness in the world? Is it not our incapability to model the complexities in modelling the coin toss correctly that is leading to this probaility explanation?

If we were to know exactly the intial conditions and the physics of tossin the coin, we should certainly be able to predict the outcome, without having to to resort to any probabilistic explanation.. so where does probability come into the picture in our coin tossing experiment?

Now let's change the experiment slightly.. let's say 1000 people are given the coins and are asked to toss without any other instructions.. then, we wud intuitively expect half the outcomes to be heads and the other half to be tails! and well, it actually does turn out to be true..

Why does this happen? as mentioned earlier, for any single toss, the outcome is not random, but is a function of how we toss the coin and what the experimental conditions are.. so there seems to be no reason to expect half the outcomes to be heads and the other half tails!! shouldn't the outcome depend on the mood of the individuals selected for the experiment and on the experimental conditions??
But assuming a random selection of individuals and normal experimental conditions, the outcome almost always adheres to our basic intuition.. so what's happening here?

Guess the theory says that the small disturbances in the experimental conditions, which affect the outcome, can be modelled as random noise which will determine the outcome as either heads or tails with equal probability and it turns out to be truel in reality.. so, in effect, our inability to exactly model the process, is overcome with this wonderful probability theory. and very often, we really don't need all the fine details of the physical process for our applications.. so we can save all our energies and time by cleverly incorporating this theory of probability!!