NCERT Class 12 · Ch 13 Exercise 13.1 · Q11
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.1 Question 11
For a fair die, E={1,3,5}, F={2,3}, G={2,3,4,5}. Find (i) P(E|F),P(F|E), (ii) P(E|G),P(G|E), (iii) P(E∪F|G),P(E∩F|G).
💡 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) 1/2,1/3; (ii) 1/2,2/3; (iii) 3/4,1/4.
- Use |event∩condition|/|condition| because the six outcomes are equally likely.
- Intersections: E∩F={3}, E∩G={3,5}, (E∪F)∩G={2,3,5}, (E∩F)∩G={3}.
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