If we know (or assume) events are [[independent]], we can simply multiply the marginal probabilities of each event to calculate the probability of both events occurring $P(A \cap B) = P(A) * P(B)$ This is a simple consequence of assuming the term $P(A \cup B)$ in the definition of [[joint probability]] below is $0$. $P(A \cap B) = P(A) * P(B) - P(A \cup B)$