Question:
If A and B are independent events, then:
If A and B are independent events, then:
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Exam Tip:
Independence means: \[ P(A \cap B) = P(A)P(B) \] This does not require \(P(A \cap B) > 0\).
Independence means: \[ P(A \cap B) = P(A)P(B) \] This does not require \(P(A \cap B) > 0\).
Updated On: Aug 27, 2026
- A and B are independent
- A and B are dependent
- \(P(A \cap B) > 0\)
- \(P(A \cap B) \neq 0\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
The question states: "If A and B are independent events, then:"
This is a tautological statement.
If A and B are independent, then they are independent by definition.
Step 2: Analyzing the Options:
• (A) A and B are independent: True by definition.
• (B) A and B are dependent: False, they are independent.
• (C) \(P(A \cap B) > 0\): Not necessarily. If \(P(A) = 0\) or \(P(B) = 0\), then \(P(A \cap B) = 0\).
• (D) \(P(A \cap B) \neq 0\): Not necessarily.
Step 3: Final Answer:
Therefore, option (A) is correct.
The question states: "If A and B are independent events, then:"
This is a tautological statement.
If A and B are independent, then they are independent by definition.
Step 2: Analyzing the Options:
• (A) A and B are independent: True by definition.
• (B) A and B are dependent: False, they are independent.
• (C) \(P(A \cap B) > 0\): Not necessarily. If \(P(A) = 0\) or \(P(B) = 0\), then \(P(A \cap B) = 0\).
• (D) \(P(A \cap B) \neq 0\): Not necessarily.
Step 3: Final Answer:
Therefore, option (A) is correct.
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