Question

Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is:

• A. between 0 and 1
• B. 0
• C. 1
• D. 0.5

Hint:

For mutually exclusive events, \(P(A \cap B) = 0\).
The conditional probability \(P(B|A) = 0\) if \(A\) has occurred.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Mutually exclusive events cannot occur at the same time.
If A has occurred, B cannot occur.

Step 2: Key Approach:
Use the definition of mutually exclusive events.

Step 3: Detailed Explanation:
Mutually exclusive means \(P(A \cap B) = 0\).
Given that event A has occurred, the sample space is reduced to A.
Since A and B are mutually exclusive, \(P(B | A) = 0\).
Thus, the probability of B occurring given A is 0.
This is option (B).
Mutually exclusive events are disjoint.
If one occurs, the other is impossible.