NCERT Class 12 · Ch 13 Miscellaneous Exercise · Q9
NCERT Class 12 Maths · Chapter 13 Probability · Miscellaneous Exercise Question 9
Subsystem failure probabilities: P(A)=0.2, P(B alone)=0.15, P(A∩B)=0.15. Find (i) P(A|B), (ii) P(A alone).
💡 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: (i) 1/2; (ii) 1/20.
- P(B)=P(B alone)+P(A∩B)=0.15+0.15=0.30.
- P(A|B)=0.15/0.30=1/2. P(A alone)=0.20−0.15=0.05=1/20.
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