Which of the following statements best describes the addition rule of probability?

• A. The probability that either event A or event B occurs is equal to the sum of their probabilities minus the probability that both events occur: $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$.
• B. The probability that neither event A nor event B occurs is equal to one minus the sum of their probabilities: $P(notA\cap notB)=1-P\left(A\right)-P\left(B\right)$.
• C. The probability that both event A and event B occur is equal to the sum of their probabilities: $P(A\cap B)=P\left(A\right)+P\left(B\right)$.
• D. The probability that either event A or event B occurs is equal to the product of their probabilities: $P(A\cup B)=P\left(A\right)\times P\left(B\right)$.

Answer: (A)

Verified step by step guidance

1. Understand that the addition rule of probability is used to find the probability that either event A or event B (or both) occurs.
2. Recall the formula for the addition rule: \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\), where \(P(A \cup B)\) is the probability that A or B occurs, \(P(A)\) and \(P(B)\) are the probabilities of each event individually, and \(P(A \cap B)\) is the probability that both events occur together.
3. Recognize why we subtract \(P(A \cap B)\): because when adding \(P(A)\) and \(P(B)\), the overlap where both events happen is counted twice, so we need to subtract it once to avoid double counting.
4. Compare this correct formula to the other options, noting that the probability of neither event occurring or the product of probabilities relates to different rules or concepts (complement rule and multiplication rule, respectively).
5. Conclude that the best description of the addition rule is the one that states the probability of either event A or event B occurring equals the sum of their probabilities minus the probability that both occur.