Ok, a friend asked me this question before and I posted it, but I jumped the gun a bit so I am going to rephrase the question with a bit more detail. Personally, I love probability—maybe a bit too much (hence why i am broke :( ). Anyway, my friend posted earlier about the coin, so I am going to go back to it. Anything which has two possible outcomes always has a one in two chance of being the outcome I want. So when I flip a coin, I have a one in two chance of getting heads or tails. Now my friend seems to think that there will always be a variable that will mislead the outcome—always. So no outcome can ever be truly predicted because there is always some force that will undermine the math or experiment. He stated that this is true for anything we try to predict because something will always contaminate the experiment. He stated that the coin flip would need more math to explain on which side did the coin start, who threw it, and why would it land on what you would want it to. According to him, there are an infinite number of possibilities which would cause the coin to land on heads as there are too many variables from the basic equation and we can't predict them all. This got me thinking a bit. I still think he is wrong but could someone post a fool-proof equation so i can get him off my back? :)
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Coin flips can never be predicted individually. We say that if we took n trials of coin flips, if n is sufficiently large the probabilities will tend to the expected value. Probability and Statistics are about understanding these random events and making inferences based upon testing real data against probabilistic models. There are always errors. Look up convergence in probability to get an analytic look at why and some theory behind the probability.