Question:
A and B are events such that \( P(A \cup B) = 3/4 \), \( P(A) = 1/4 \), and \( P(A \cap B) = 2/3 \). Then the probability that \( P(A \cap B) \) is
A and B are events such that \( P(A \cup B) = 3/4 \), \( P(A) = 1/4 \), and \( P(A \cap B) = 2/3 \). Then the probability that \( P(A \cap B) \) is
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The formula for the union of two events is \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \).
Updated On: Jan 12, 2026
- \( 5/12 \)
- \( 5/8 \)
- \( 3/8 \)
- \( 1/4 \)
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The Correct Option is B
Solution and Explanation
Step 1: Use the formula for the union of two events.
The formula for the union of two events is: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substituting the known values, we solve for \( P(B) \).
Step 2: Conclusion.
Thus, the correct probability is \( 5/8 \).
Final Answer: \[ \boxed{\frac{5}{8}} \]
The formula for the union of two events is: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substituting the known values, we solve for \( P(B) \).
Step 2: Conclusion.
Thus, the correct probability is \( 5/8 \).
Final Answer: \[ \boxed{\frac{5}{8}} \]
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