Class 12 Probability · Long Answer3 Marksprobability_distributions
Class 12 Maths · Probability · Long Answer #63
X takes 1,2,3 with probabilities k/2,k/3,k/6. Find k, P(1≤X<3), and E(X).
✅ Step-by-Step Solution
Final Answer: k=1; P(1≤X<3)=5/6; E(X)=5/3
- Normalize: k(1/2+1/3+1/6)=k=1.
- P(1≤X<3)=P(X=1)+P(X=2)=1/2+1/3=5/6.
- E(X)=1·1/2+2·1/3+3·1/6=1/2+2/3+1/2=5/3.
- Thus k=1, the requested probability is 5/6, and the mean is 5/3.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Normalize: k(1/2+1/3+1/6)=k=1.
- [1 mark] P(1≤X<3)=P(X=1)+P(X=2)=1/2+1/3=5/6.
- [1 mark] E(X)=1·1/2+2·1/3+3·1/6=1/2+2/3+1/2=5/3.
- [0.5 marks] Thus k=1, the requested probability is 5/6, and the mean is 5/3.
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