1. Let's start by stating the problem: We want to understand why, when calculating the probability of the union of two events $A$ and $B$, we add their individual probabilities and then subtract the overlap (intersection) once. 2. The formula for the probability of the union of two events is: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ 3. Explanation: When we add $P(A)$ and $P(B)$, the area where $A$ and $B$ overlap (the intersection) is counted twice — once in $P(A)$ and once in $P(B)$. 4. To correct this double counting, we subtract the overlap $P(A \cap B)$ exactly once. 5. If we did not subtract the overlap, the probability of the union would be overestimated. 6. Therefore, subtracting the overlap once ensures that each part of the union is counted exactly once, giving the correct total probability. Final answer: The overlap is subtracted once to avoid counting it twice when adding $P(A)$ and $P(B)$.