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 $B)=P(A)+P(B)-P(A$ or $B)$.
Choose the correct answer below.
A. True
B. False, the probability that $A$ or $B$ will occur is $P(A$ or $B)=P(A) \cdot P(B)$.
C. False, the probability that $A$ or $B$ will occur is $P(A$ or $B)=P(A)+P(B)-P(A$ and $B)$.
D. False, the probability that $A$ or $B$ will occur is $P(A$ or $B)=P(A)+P(B)$.

Step 1 ：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 $B)=P(A)+P(B)-P(A$ or $B)$.

Step 2 ：Choose the correct answer below.

Step 3 ：A. True

Step 4 ：B. False, the probability that $A$ or $B$ will occur is $P(A$ or $B)=P(A) \cdot P(B)$.

Step 5 ：C. False, the probability that $A$ or $B$ will occur is $P(A$ or $B)=P(A)+P(B)-P(A$ and $B)$.

Step 6 ：D. False, the probability that $A$ or $B$ will occur is $P(A$ or $B)=P(A)+P(B)$.

Step 7 ：The statement is false. The correct formula for the probability of either event A or event B occurring is $P(A$ or $B)=P(A)+P(B)-P(A$ and $B)$. This is because the sum of the probabilities of A and B includes the probability of both A and B occurring, which is counted twice. Therefore, we subtract the probability of both A and B occurring once to correct for this.

Step 8 ：Final Answer: \(\boxed{C}\).