NCERT Class 12 · Ch 13 Exercise 13.2 · Q10
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.2 Question 10
P(A)=1/2,P(B)=7/12,P(A′∪B′)=1/4. State whether A,B are independent.
💡 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: The supplied probabilities are inconsistent; no such pair of events exists.
- De Morgan gives P(A∩B)=1−P(A′∪B′)=3/4.
- An intersection cannot have probability greater than either marginal, but 3/4>1/2 and 3/4>7/12. Equivalently the probability of A only would be 1/2−3/4=−1/4.
- Thus these data cannot describe events, independently or otherwise; a printed value needs correction.
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