user110391
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$$p(x) = \lim_{T \rightarrow \infty} \displaystyle \sum_{k= 1}^{T} [x]_k \times \frac 1T$$

Where $$T$$ is the total amount of tests, and $$[x]_k$$ is an Iverson bracket, equal to $$1$$ if $$x$$ came true at the $$k$$th test.

Example:

$$x$$ is the statement "the coin lands with tails facing up after being flipped". Then, you flip it once, this being the $$1$$st experiment $$(k=1)$$. If it came up heads, $$[x]_1 = 0$$, and if it came up tails, $$[x]_1 = 1$$. After flipping it for the second time, you get $$[x]_2 = 1 \oplus 0$$, and so on.

Question:

Is this a valid way to conceptualize probability? To be clear, this is simply just an attempt at a mathematical formulation of what probability is. It seems completely correct to me, but probability theory has a tendency to be counterintuitive. In the case that this is valid, I'd also like to see how this compares to other conceptualizations and formulations of probability, in whatever way(s) such a comparison can be made objectively.

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