Experimental Probability – run an experiment, count the outcomes which satisfy an event, divide by the total number of trials.
Theoretical Probability – calculate the probability; you don’t need to run the experiment.
If an experiment is well designed and implemented, increasing the number of trials will generally move experimental probability closer to theoretical probability. The randomness and variability “smooths out” with a large number of trials.
If two events, and , are disjoint sets (they have no outcomes in common, or ), then the events are called mutually exclusive and they cannot occur simultaneously.
For example, you cannot simultaneously roll an even number and a 5 on a d6 die.
If two events could occur simultaneously, they are called non-mutually exclusive.