Question

If A + B are independent events, P(A \cup B) is equal to

• A. P(A) + P(B)
• B. P(A) + P(B) - P(A \cap B)
• C. P(A) \cdot P(B)
• D. None of these

Hint:

For two independent events A and B, the probability of their union is P(A \cup B) = P(A) + P(B) - P(A \cap B) .

Answer 1

The Correct Option is B

Step 1: Understanding the formula.
For two events A and B, the probability of the union of these events is given by the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Step 2: Checking the independence.
If A and B are independent events, then: \[ P(A \cap B) = P(A) \cdot P(B) \] So, the formula for the union remains the same. Step 3: Conclusion.
Thus, the correct formula is P(A \cup B) = P(A) + P(B) - P(A \cap B) . Final Answer: P(A) + P(B) - P(A \cap B) .