Question

For two events A and B, $P(A)=P(A/B)=1/4$ and $P(B/A)=1/2$. Then

• A. A and B are mutually exclusive
• B. A and B are dependent
• C. $P(\bar{A}/B)=3/4$
• D. None of the above

Hint:

For two events A and B, $P(A)=P(A/B)=1/4$ and $P(B/A)=1/2$. Then

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
If $P(A/B) = P(A)$, then A and B are independent events.
Step 2: Evaluation
We are given $P(A/B) = 1/4$.
Step 3: Final Calculation
By the complement rule for conditional probability, $P(\bar{A}/B) = 1 - P(A/B)$.
Step 4: Conclusion
$P(\bar{A}/B) = 1 - 1/4 = 3/4$.
Hence, the Answer is: (c)