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What is the difference between independent events and mutually exclusive events?
Independent events are events which are not connected; for example, my choice of food for lunch will have no affect on your choice of a shirt to wear in the morning. Mutually exclusive events are connected. If one happens, the other can't happen. For example, let us say that you are flying an airplane and you have a choice of airports at which you can land. If you land at one airport, you will therefore not land at the other airport, because you can land at only one airport at a time (although you can still land at other airports in the future). At a given time, the events of landing at airport A and landing at airport B are mutually exclusive.
Do you multiply for dependent events?
No, you multiply for independent events.
If A and B are independent events than A and B' are independent?
Yes.
What are dependent and independent probability in math terms?
Two events are said to be independent if the outcome of one event does not affect the outcome of the other. Their probabilities are independent probabilities. If the events are not independent then they are dependent.
What events are such that the occurrence of one does not change the probability of other events?
Independent events.
