NCERT Class 12 · Ch 13 Miscellaneous Exercise · Q13
NCERT Class 12 Maths · Chapter 13 Probability · Miscellaneous Exercise Question 13
If P(A)+P(B)−P(A∩B)=P(A), which listed conditional identity 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: If P(B)>0, B: P(A|B)=1. With the printed assumptions alone, that conditional may be undefined.
- Cancel P(A) to get P(B)=P(A∩B), equivalently P(B∖A)=0.
- For P(B)>0, divide to obtain P(A|B)=1.
- The premise also permits B=∅, when P(B)=0 and P(A|B) is undefined. A nonzero conditioning probability is missing from the printed question.
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