NCERT Class 12 · Ch 13 Exercise 13.1 · Q17
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.1 Question 17
If P(A|B)=P(B|A), which listed conclusion follows?
💡 Concept Hints
- Define the events and identify which event is being conditioned on.
- Use P(E|F)=P(E∩F)/P(F), or separate the possible sources before applying total probability and Bayes.
✅ Step-by-Step Solution
Final Answer: None follows universally. D follows if the common intersection probability is positive.
- Assuming P(A),P(B)>0, equality says P(A∩B)/P(B)=P(A∩B)/P(A). If the intersection has positive probability, cancellation gives P(A)=P(B).
- If the intersection is zero, both conditionals are zero even with different marginals. For disjoint events with P(A)=1/4,P(B)=1/2, D fails.
- Conversely A=B with positive probability satisfies the equality without an empty intersection, so C is not universally forced either. The positive-intersection assumption is missing.
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