Class 12 Probability · Short Answer2 Marksindependence
Class 12 Maths · Probability · Short Answer #39
Prove that if E,F are independent, then E,F′ are independent.
✅ Step-by-Step Solution
Final Answer: E and F′ are independent.
- Independence gives P(E∩F)=P(E)P(F).
- Since E is the disjoint union of E∩F and E∩F′, P(E∩F′)=P(E)−P(E∩F)=P(E)[1−P(F)].
- Thus P(E∩F′)=P(E)P(F′), proving independence, including zero-probability cases.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Independence gives P(E∩F)=P(E)P(F).
- [1 mark] Since E is the disjoint union of E∩F and E∩F′, P(E∩F′)=P(E)−P(E∩F)=P(E)[1−P(F)].
- [0.5 marks] Thus P(E∩F′)=P(E)P(F′), proving independence, including zero-probability cases.
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