I am not sure if this can be determined, but I was wondering if there was any way to go deeper into probability to find the odds that your experimental results match your theoretical results.
For example, we know that if a fair die is rolled there is a 1 in 6 chance that it will come up 3 (arbitrary). So, if it is rolled 6 times, what are the odds that this will hold true and a three will come up exactly once?
Thanks
We will assume that the theoretical model fits the reality well. This is the case for the dice example of the post.
The probability of exactly one $3$ can be computed explicitly, since the number of $3$'s in $6$ tosses has Binomial Distribution (please see Wikipedia for details). This probability is $$\binom{6}{1}\left(\frac{6}{1}\right)^1\left(\frac{5}{6}\right)^5,$$ where $\binom{6}{1}=6$. Computation shows that this is approximately $0.4$, not very big, but not terribly small.
If we toss $18000$ times, the probability of exactly $3000$ $3$'s is quite small. However, let $N$ be the number of $3$'s in $18000$ tosses. Then the ratio $\frac{N}{18000}$ will likely be quite close to $\frac{1}{6}$. One can state quite precisely how likely and how close. For example, with probability about $0.99$, the ratio $\frac{N}{18000}$ will be no more than $0.0072$ away from $\frac{1}{6}$.
For a more detailed discussion of related matters, please see the Wikipedia article on The Law of Large Numbers.