Question:
If A and B are mutually exclusive events, then:
If A and B are mutually exclusive events, then:
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Exam Tip:
• Mutually Exclusive: \(P(A \cap B) = 0\), \(P(A \cup B) = P(A) + P(B)\).
• Independent: \(P(A \cap B) = P(A)P(B)\), \(P(A \cup B) = P(A) + P(B) - P(A)P(B)\).
• Mutually Exclusive: \(P(A \cap B) = 0\), \(P(A \cup B) = P(A) + P(B)\).
• Independent: \(P(A \cap B) = P(A)P(B)\), \(P(A \cup B) = P(A) + P(B) - P(A)P(B)\).
Updated On: Aug 27, 2026
- \(P(A \cap B) = 0\)
- \(P(A \cap B) = P(A)P(B)\)
- \(P(A \cup B) = 0\)
- \(P(A \cup B) = P(A)P(B)\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Mutually exclusive events are events that cannot occur at the same time.
This means they have no outcomes in common.
Step 2: Key Definition:
If A and B are mutually exclusive, then \(A \cap B = \emptyset\).
Therefore, \(P(A \cap B) = 0\).
Step 3: Analyzing the Options:
• (A) \(P(A \cap B) = 0\): True.
• (B) \(P(A \cap B) = P(A)P(B)\): This is true only if A and B are independent, not mutually exclusive.
• (C) \(P(A \cup B) = 0\): False. \(P(A \cup B) = P(A) + P(B)\) for mutually exclusive events.
• (D) \(P(A \cup B) = P(A)P(B)\): False. This is the formula for independent events, not mutually exclusive.
Step 4: Final Answer:
Therefore, option (A) is correct.
Mutually exclusive events are events that cannot occur at the same time.
This means they have no outcomes in common.
Step 2: Key Definition:
If A and B are mutually exclusive, then \(A \cap B = \emptyset\).
Therefore, \(P(A \cap B) = 0\).
Step 3: Analyzing the Options:
• (A) \(P(A \cap B) = 0\): True.
• (B) \(P(A \cap B) = P(A)P(B)\): This is true only if A and B are independent, not mutually exclusive.
• (C) \(P(A \cup B) = 0\): False. \(P(A \cup B) = P(A) + P(B)\) for mutually exclusive events.
• (D) \(P(A \cup B) = P(A)P(B)\): False. This is the formula for independent events, not mutually exclusive.
Step 4: Final Answer:
Therefore, option (A) is correct.
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