Determine whether the following statement is true or false. If it is false, explain why. The probability that event \( A \) or event \( B \) will occur is \( P(A \) or \( B)=P(A)+P(B)+P(A \) and \( B) \) Choose the correct answer below. A. True B. False, the probability that \( A \) or \( B \) will occur is \( P(A \) or \( B)=P(A)+P(B) \). C. False, the probability that \( A \) or \( B \) will occur is \( P(A \) or \( B)=P(A) \cdot P(B) \). D. False, the probability that \( A \) or \( B \) will occur is \( P(A \) or \( B)=P(A)+P(B)-P(A \) and \( B) \).

The correct answer is D. False, the probability that \( A \) or \( B \) will occur is \( P(A \) or \( B)=P(A)+P(B)-P(A \) and \( B) \). This formula accounts for the potential overlap between events \( A \) and \( B \). If both events can occur simultaneously, adding \( P(A) \) and \( P(B) \) would double-count the probability of their intersection \( P(A \) and \( B) \). Therefore, we subtract \( P(A \) and \( B) \) to correct for this overlap, giving us the accurate probability of either event happening. Probability can seem tricky at first, but just think of it like a party: if two friends both invite the same guest, you wouldn't want to count that guest twice when estimating how many people will show up! They should only be counted once!