Sometimes it is possible to define a model for a trial or experiment and then use mathematical or scientific rules to determine the probability of the possible outcomes. Such a procedure gives theoretical probabilities.
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Theoretical implies the mathematical calculation of the probability. Empirical means the actual outcomes to happen.
The probability of an event may be measured experimentally or theoretically. In experimental probability, an experiment is conducted repeatedly. The probability of the event is the number of experiments in which the event occurs as a proportion of the number of times the experiment is conducted. By contrast, the theoretical probability is calculated from theoretical models and laws of science (and some assumptions about unbiased/fairness).
It means that you think about it but you don't actually do it.
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principal(in terms of math)- the amount you borrow or deposit