Posted: Nov 18, 2018 7:24 pm
BWE wrote:surreptitious57 wrote:Probability works because it attempts to model reality based on observation
Every probability exists between 0 and I and how accurate a prediction will
be is determined by the accuracy and completeness of the data in question
You toss a coin I00 times probability says it will land heads 50 times and tails 50 times
Reality however says it is 5I / 49 because one side is marginally heavier than the other
But these are all tautological answers. My question is why does the coin flip vary around a bell curve? Why wouldn't it be always heads for no reason at all?
Coin flips are not distributed by a bell curve (AKA Normal distribution or Gaussian distribution), they are binomial distributions.
There's an important theorem in mathematics that governs the distribution of sample means from a wide range of arbitrary distributions, known as the https://en.wikipedia.org/wiki/Central_limit_theorem, which says that for large sample sizes the distribution of sample means is approximately normal regardless of the shape of the original distributions.
In terms of the question "Why wouldn't it be always heads for no reason at all?" it's poorly phrased. A series of coin flips of a fair coin of arbitrary length might be all heads, probability theory does not forbid this. And similarly a coin might be biased (such as by having two heads) such that it only ever flips heads. However in this latter situation the assumption that the coin is fair does not hold, and a model is only as good as its assumptions.