Class 12 Probability · Long Answer3 Marksprobability_distributions

Class 12 Maths · Probability · Long Answer #113

Select3 distinct numbers uniformly from {1,2,3,4,5,6}. X is their maximum. Find its distribution and mean.

✅ Step-by-Step Solution

Final Answer: P(X=3)=1/20; P(X=4)=3/20; P(X=5)=3/10; P(X=6)=1/2. Mean=21/4.

There are C(6,3)=20 equally likely subsets; the maximum ranges from3 to6.
For maximum k include k and choose the other2 from {1,…,k−1}. Counts C(k−1,2) are1,3,6,10. The probabilities are P(X=3)=1/20; P(X=4)=3/20; P(X=5)=3/10; P(X=6)=1/2. Their sum is 1.
E(X)=ΣxP(X=x)=(3)(1/20)+(4)(3/20)+(5)(3/10)+(6)(1/2)=21/4.
P(X=3)=1/20; P(X=4)=3/20; P(X=5)=3/10; P(X=6)=1/2. Mean=21/4.

[0.5 marks] There are C(6,3)=20 equally likely subsets; the maximum ranges from3 to6.
[1 mark] For maximum k include k and choose the other2 from {1,…,k−1}. Counts C(k−1,2) are1,3,6,10. The probabilities are P(X=3)=1/20; P(X=4)=3/20; P(X=5)=3/10; P(X=6)=1/2. Their sum is 1.
[1 mark] E(X)=ΣxP(X=x)=(3)(1/20)+(4)(3/20)+(5)(3/10)+(6)(1/2)=21/4.
[0.5 marks] P(X=3)=1/20; P(X=4)=3/20; P(X=5)=3/10; P(X=6)=1/2. Mean=21/4.

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