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. \( 5/12 \)
• B. \( 5/8 \)
• C. \( 3/8 \)
• D. \( 1/4 \)

Hint:

The formula for the union of two events is \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \).

Answer 1

The Correct Option is B

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: \[ \boxed{\frac{5}{8}} \]