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Theoretical implies the mathematical calculation of the probability. Empirical means the actual outcomes to happen.
The theoretical probability provides a model for predicting the outcome of trials. You then carry out a number of trials. Compare the outcome of your trials with the results predicted by the theoretical model. The comparison will usually involve "hypothesis testing", a branch of statistics. This is a method to test how likely the actual outcomes are if the theoretical probabilities were true. The exact nature of the test will depend on the theoretical basis and so the answer cannot be simplified.
It means that you think about it but you don't actually do it.
I think it means to find the theoretical probability of something random that has results that are numbers. For instance, rolling a die and trying to get a 6 is a "chance activity with numerical outcomes".
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