# how to calculate cumulative probability for *dependent* events?

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.

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, $$P(AB) = P(A) \cdot P(B | A) = P(B) \cdot P(A | B)$$.