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The formula for cumulative probability for independent events is easy enough. Just multiply the probability of the events together. For example, 2 independent events, each with a probability of 0.80 would have a cumulative probability of 0.8 * 0.8 = 0.64. But I need to figure out the formula to determine cumulative probability for dependent events. For example, what is the probability of both Event A and Event B occuring if they are both dependent on each other? Let's say that Event A has a probability of .80 and Event B has a probability of 0.90.

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In this case you can say that $0.7 \leqslant P(AB) \leqslant 0.8$, and nothing else - for any number $x \in [0.7, 0.8]$ there are events $A$ and $B$ with $P(A) = 0.8$, $P(B) = 0.9$, $P(AB) = x$.

There is also notion of conditional probability - by definition, $P(AB) = P(A) \cdot P(B | A) = P(B) \cdot P(A | B)$.

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