Question

If \( P(A) = \frac{1}{2}, P(B) = \frac{5}{12} \) and \( P(B/A) = \frac{1}{15} \), then \[ P(A \cup B) \] is equal to

• A. \( \frac{89}{180} \)
• B. \( \frac{90}{180} \)
• C. \( \frac{91}{180} \)
• D. \( \frac{92}{180} \)

Hint:

Use the formula \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \) to find the probability of the union of two events.

Answer 1

The Correct Option is C

Step 1: Using the formula for \( P(A \cup B) \).
We can calculate \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \). Using the given information, \( P(A \cap B) = P(B/A) \times P(A) \).

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer: \[ \boxed{\text{(C) } \frac{91}{180}} \]