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We need a few notes on the relative frequency idea of probability. Suppose we want to determine the probability of some event A. Suppose that we can repeat the experiment over and over again, such that the trials are:
Let N be the number of trials and let #(A) denote the number of times A occurred. Then
- Independent of one another.
- Identical , in that conditions do not change from one trial to another.
and the approximation gets better as N gets larger. Note that the relative frequency idea of probability obeys the three axioms of probability.
The probability of A