Question

If \(P(A) = \frac{1}{2}\), \(P(B) = \frac{1}{3}\), and \(P(A \cap B) = \frac{1}{6}\), then \(P(A \cup B)\) is: 

• A. \(2/7\)
• B. \(1/7\)
• C. \(4/7\)
• D. \(2/3\)

Hint:

Exam Tip:
For any two events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] If they are mutually exclusive, \(P(A \cap B) = 0\), so \(P(A \cup B) = P(A) + P(B)\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
We need to find the probability of the union of two events A and B.

Step 2: Key Formula or Approach:
The formula for the union of two events is: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Step 3: Detailed Explanation:
Given: \(P(A) = \frac{1}{2}\), \(P(B) = \frac{1}{3}\), \(P(A \cap B) = \frac{1}{6}\).
\[ P(A \cup B) = \frac{1}{2} + \frac{1}{3} - \frac{1}{6} = \frac{3}{6} + \frac{2}{6} - \frac{1}{6} = \frac{4}{6} = \frac{2}{3} \]

Step 4: Final Answer:
Therefore, option (D) is correct.