Probability and proof of a coin toss I don't know how to ask this more generally. So I will use the classic example of a coin toss. My question is, as the number of experiments of a coin toss goes to infinity, is there a mathematical proof that the probability of getting a heads or a tails does indeed go to 1/2?
 A: It's so called Borel's law of large numbers, you can look here
A: When you take the number of times you got heads (or tails) and divide it by the number of times you made a toss (let's say n), the result becomes a random variable itself, which if I'm not mistaken is defined as the frequency. If p is the theoretical probability of getting heads (or tails), then the expected value (or the mean) of the frequency is p, and its standard deviation is proportional to $\frac{1}{\sqrt n}$, which in theory means the frequency approaches p as n goes to infinity.
This comes from the law of large numbers, and the definition of p itself as the number of times you got heads (or tails, or a success in any experiment involving a random variable) divided by the number of tosses (or times you experimented) as they approach infinity also arises from this.
If you were talking about a mathematical proof that shows that this limit is actually $\frac{1}{2}$ without infering it from experiments (or reason, I guess), I don't know if there exists such proof. I'm sorry.
