What is the difference between non-mutually exclusive
event and a independent event?
Two non-mutually exclusive events mean that both can happen at
the same time.
For example, you got a class of students of all gender and
races. A is the probability of picking a male student and B is the
probability of picking a chinese student. Both events are
non-mutually exclusive as you can pick a student who is male and
chinese at the same time.
Two independent events mean that their occurrence will
not affect each other.
For example, A means throwing a 6 with a dice on the first
throw, B means throwing a 3 with a dice
on the second
throw. No matter A happens or not, it will not
affect the probability of B, hence they are independent events.