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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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