Question:
For two events A and B, $P(A)=P(A/B)=1/4$ and $P(B/A)=1/2$. Then
For two events A and B, $P(A)=P(A/B)=1/4$ and $P(B/A)=1/2$. Then
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For two events A and B, $P(A)=P(A/B)=1/4$ and $P(B/A)=1/2$. Then
Updated On: Apr 15, 2026
- A and B are mutually exclusive
- A and B are dependent
- $P(\bar{A}/B)=3/4$
- None of the above
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The Correct Option is C
Solution and Explanation
Step 1: Concept
If $P(A/B) = P(A)$, then A and B are independent events.
Step 2: Analysis
We are given $P(A/B) = 1/4$.
Step 3: Evaluation
By the complement rule for conditional probability, $P(\bar{A}/B) = 1 - P(A/B)$.
Step 4: Conclusion
$P(\bar{A}/B) = 1 - 1/4 = 3/4$.
Final Answer: (c)
If $P(A/B) = P(A)$, then A and B are independent events.
Step 2: Analysis
We are given $P(A/B) = 1/4$.
Step 3: Evaluation
By the complement rule for conditional probability, $P(\bar{A}/B) = 1 - P(A/B)$.
Step 4: Conclusion
$P(\bar{A}/B) = 1 - 1/4 = 3/4$.
Final Answer: (c)
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