An experiment is a controlled operation that yields a set of results.
The possible results of an experiment are called outcomes
An event is a set of outcomes.
Empirical probability is probability determined by performing an experiment a number of times and observing the results.
Theoretical Probability is determined by studying the possible outcomes that can occur.
P(E) is the probability that event E occurs.
For Empirical Probability:
number of times event E occurred
P(E) = ------------------------------------------------
the number of times the experiment was conducted
Empirical probability is used when the probabilities can not be computed theoretically.
The Law of Large Numbers states that probability statements apply in practice to a large number of trials, not to a single trial. It is the relative frequency over the long run that is accurately predictable, not individual events or precise totals.
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12.2 Theoretical Probability
Unless stated otherwise, we will use theoretical probability from now on.
If each outcome of an experiment has the same chance of occurring as any other outcome, then the outcomes are equally likely
P(E) = n(E) / n(U). If all outcomes are equally likely
P(E) = 0 iff E can not occur
P(E) = 1 iff E must occur
0 ≤ P(E) ≤ 1
The sum of the probabilities of all possible outcomes of an experiment is 1