NCERT Class 12 · Ch 13 Miscellaneous Exercise · Q11
NCERT Class 12 Maths · Chapter 13 Probability · Miscellaneous Exercise Question 11
If P(A)≠0 and P(B|A)=1, which listed set relation 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: P(A∖B)=0. Option A follows as an actual set inclusion only with an additional no-null-outcomes assumption.
- P(B|A)=1 gives P(A∩B)=P(A), hence P(A∖B)=0.
- A nonempty set can have probability zero. For a finite example with outcome weights 1/2,1/2,0, take A={1,3},B={1}. Then P(B|A)=1 but A is not contained in B.
- If every outcome in a finite sample space has positive probability, probability-zero difference must be empty and the intended inclusion A⊆B follows.
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