The problem requires determining whether the statement about the probability of the union of two events $A$ and $B$ is correct.

The correct formula for the probability of either event $A$ or $B$ occurring (i.e., $P(A \text{ or } B)$) is:

$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

This formula accounts for the overlap between events $A$ and $B$ by subtracting $P(A \text{ and } B)$, the probability that both events occur simultaneously, to avoid double-counting that shared region.

Now let's analyze the given statement:

The probability that event $A$ or event $B$ will occur is $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ or } B)$.

This expression is incorrect because the term that should be subtracted is $P(A \text{ and } B)$, not $P(A \text{ or } B)$. Thus, the correct answer is option D:

False, the probability that $A$ or $B$ will occur is $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$.

Would you like further details on probability rules, or do you have any questions?

Related Questions:

1. How is the probability of the intersection of two events $A$ and $B$ defined?
2. What is the probability formula for mutually exclusive events?
3. Can you explain the concept of conditional probability with examples?
4. How do probabilities change if events are independent?
5. What is the difference between union and intersection in probability?

Tip:

When working with probabilities of combined events, always check if the events are independent or mutually exclusive to apply the correct formulas.