Independent events

Events are independent when knowing that one happened tells you nothing about the other, so $P(A \mid B) = P(A)$ (the probability of $A$ given $B$ equals the probability of $A$). For independent events the multiplication rule gives $P(A \text{ and } B) = P(A) \times P(B)$. For example, two fair coin flips are independent, so the probability of two heads is $0.5 \times 0.5 = 0.25$. Independence is about influence, not overlap, so do not confuse it with mutually exclusive.