Question

If $A$ and $B$ are independent events, then $P(A \cap B)$ is:

• A. $P(A) + P(B)$
• B. $P(A) \cdot P(B)$
• C. $P(A) / P(B)$
• D. $P(A) - P(B)$

Hint:

For independent events, "And" means multiply.

Answer 1

The Correct Option is B

Step 1: Concept
Independent events are those where the occurrence of one does not affect the probability of the other.
Step 2: Analysis
By definition, for independent events $A$ and $B$, $P(B|A) = P(B)$.
Applying multiplication theorem: $P(A \cap B) = P(A) \cdot P(B|A)$.
Step 3: Conclusion
$P(A \cap B) = P(A) \cdot P(B)$.
Final Answer: (B)