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Ten red balls, ten blue balls.
First draw, P(red) = 50%
once that draw is done (let's assume I picked red), and if I do not put that red ball back in the bag, then the probability on the second draw is
P(red) = 47.4%
this is NOT an independent event.
If I had picked blue on the first draw, then the probability of red on the second draw is 52.6%
In either case, it is no longer 50%. The outcome of the first draw affects the second draw, therefore the second draw is NOT independent from the first draw (even though, in this case, it is not a mutually exclusive event).
Mutually exclusive just happens to be an extreme case.