Class 12 Probability · Short Answer2 Marksevent_algebra
Class 12 Maths · Probability · Short Answer #101
Let p=P(A∪B) and q=P(exactly one of A,B occurs). Prove P(A′)+P(B′)=2−2p+q.
✅ Step-by-Step Solution
Final Answer: P(A′)+P(B′)=2−2p+q
- Write r=P(A∩B). The union is the disjoint union of exactly-one and both, so p=q+r and r=p−q.
- The addition rule gives P(A)+P(B)=p+r=2p−q.
- Taking complements gives P(A′)+P(B′)=2−[P(A)+P(B)]=2−2p+q.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write r=P(A∩B). The union is the disjoint union of exactly-one and both, so p=q+r and r=p−q.
- [1 mark] The addition rule gives P(A)+P(B)=p+r=2p−q.
- [0.5 marks] Taking complements gives P(A′)+P(B′)=2−[P(A)+P(B)]=2−2p+q.
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