Addition Rule vs Multiplication Rule

The general addition rule is $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, where $\cup$ is the union symbol (A or B) and $\cap$ is the intersection symbol (A and B). You subtract the overlap because every outcome sitting in both events was already counted once in $P(A)$ and a second time in $P(B)$. That subtraction disappears only when the two events are mutually exclusive, because then they share no outcomes and $P(A \cap B) = 0$. Drawing one card from a standard 52-card deck, $P(\text{heart or king}) = 13/52 + 4/52 - 1/52 = 16/52 \approx 0.3077$.

For independent events the rule is $P(A \cap B) = P(A)P(B)$, where $\cap$ is the intersection symbol (A and B). Independence means learning that one event happened does not change the probability of the other, so the second factor never has to be adjusted. Flipping a fair coin and rolling a fair die are independent, so $P(\text{heads and a 6}) = 0.5 \times 1/6 = 1/12 \approx 0.0833$. If the events are not independent you must use the general multiplication rule with a conditional probability instead.