If two events A and B are mutually exclusive in economics, which of the following statements is true?

• A. The occurrence of A prevents the occurrence of B.
• B. A and B can occur simultaneously.
• C. A and B are independent events.
• D. The probability of both A and B occurring together is greater than zero.

Answer: (A)

Verified step by step guidance

1. Understand the definition of mutually exclusive events: Two events A and B are mutually exclusive if they cannot occur at the same time. This means that if event A happens, event B cannot happen simultaneously, and vice versa.
2. Express this concept mathematically: For mutually exclusive events, the probability of both A and B occurring together is zero. This can be written as \(P(A \cap B) = 0\).
3. Analyze the given statements in light of this definition: Since \(P(A \cap B) = 0\), the statement 'The probability of both A and B occurring together is greater than zero' is false.
4. Check the statement about independence: Independent events satisfy \(P(A \cap B) = P(A) \times P(B)\), which is generally not zero unless one event has zero probability. Since mutually exclusive events cannot occur together, they are not independent unless one event is impossible.
5. Conclude which statement is true: The statement 'The occurrence of A prevents the occurrence of B' aligns perfectly with the definition of mutually exclusive events, making it the correct choice.