Question

If $A$ and $B$ are two events such that $P(A) = 0.4, P(B) = 0.8$ and $P(B|A) = 0.6$, then $P(A \cup B)$ is:

• A. 0.96
• B. 0.24
• C. 0.56
• D. 0.66

Hint:

Conditional probability $P(B|A)$ tells you how much of $A$ is shared with $B$.

Answer 1

The Correct Option is A

Step 1: Concept
Use the definitions: $P(A \cap B) = P(A)P(B|A)$ and $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
Step 2: Analysis
$P(A \cap B) = 0.4 \times 0.6 = 0.24$. $P(A \cup B) = 0.4 + 0.8 - 0.24$.
Step 3: Conclusion
$P(A \cup B) = 1.2 - 0.24 = 0.96$.
Final Answer: (A)