Laws of large numbers (LLN's) specify what 'become deterministic' means.
They only operate within the extended model, in other words, laws of large numbers don't apply to the real world
Let's talk about Markov bounds, chebychev bounds and chernoff bounds. what it says is if Y is a non-negative R.V. with an expectation E[Y], then for any real y greater than 0, the probability that Y is greater than or equal to y is less than or equal to the expected value of Y divided by y. The proof of it is by picture.
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