Not necessarily. In fact, in binary situations they can be totally dependent - depends on the experiment.
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Mutually exclusive means they are independent of one another. So, the two events are independent of one another.
Yes.
No, independence means they are not related. Mutually exclusive means they cannot occur at the same time.
The definition of mutually exclusive events is that the events can't occur at the same time. For example, you can't flip a coin and get a head and a tail; they are mutually exclusive events.
No, if two events are mutually exclusive, they cannot both occur. If one occurs, it means the second can not occur.