Class 12 Probability · Short Answer2 Marksevent_algebra
Class 12 Maths · Probability · Short Answer #98
Events A,B are claimed to satisfy P(A)=1/2, P(B)=7/12 and P(A′∪B′)=1/4. Can such events exist, and can their independence be assessed?
✅ Step-by-Step Solution
Final Answer: No such events exist.
- By De Morgan, P(A′∪B′)=1−P(A∩B), so the stated value implies P(A∩B)=3/4.
- But an intersection cannot have probability greater than either event; 3/4>1/2=P(A) and also >7/12=P(B).
- The data are inconsistent, so no probability model exists and no meaningful independence test can be applied.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] By De Morgan, P(A′∪B′)=1−P(A∩B), so the stated value implies P(A∩B)=3/4.
- [1 mark] But an intersection cannot have probability greater than either event; 3/4>1/2=P(A) and also >7/12=P(B).
- [0.5 marks] The data are inconsistent, so no probability model exists and no meaningful independence test can be applied.
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