Originally Posted by
CaptainBlack It is the standard frequentist definition of probability of outcome $\displaystyle x$. If you
repeat the experiment a large number $\displaystyle n$ of times, and record $\displaystyle n_0$ occurences
of out come $\displaystyle x$ we estimate the probability of $\displaystyle x$ as:
$\displaystyle
\hat{p}(x) = \frac{n_0}{n}
$
Then the definition of the probability of $\displaystyle x$ is the limit of such an estimator as $\displaystyle n \to \infty$.
This can be written as:
$\displaystyle
p(x)=\lim_{n \to \infty} \frac{n_0}{n}
$
but this is a abuse of notation from other parts of mathematics as this limit
is not the usual limit encountered in other parts of mathematics, and cannot
be evaluated.
(Just learn it, you will need it for your exam, but it is nonsense. There are
better defintions that you will encounter if you contine with the study of
probability)
RonL