Disjoint vs. Independent
Disjoint
Two events that are disjoint (mutually exclusive) cannot happen at the same time.
So disjointness is about events happening at the same time. Therefore, if events A and B are disjoint, probability of A and B is 0.
If events A and B are disjoint, Then, P(A and B) = 0.
Independent
Two processes are independent if knowing the outcome of one provides no useful information about the outcome of the other.
So independence is about processes not affecting each other. Therefore, if events A and B are independent, probability of A given B is equal to the probability of A.
If events A and B are independent. Then, P(A | B) = P(A).
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