Class 12 Probability · Long Answer3 Marksprobability_distributions

Class 12 Maths · Probability · Long Answer #110

X is the number of colleges granting admission to an applicant. Its probabilities are kx for x=0,1; 2kx for x=2; k(5−x) for x=3,4; and0 otherwise. Find k and P(X=1),P(X≤2),P(X≥2).

✅ Step-by-Step Solution

Final Answer: k=1/8; P(X=1)=1/8; P(X≤2)=5/8; P(X≥2)=7/8

The masses for X=0,1,2,3,4 are 0,k,4k,2k,k; their sum 8k must equal1.
Thus k=1/8 and the distribution is (0,1/8,1/2,1/4,1/8).
P(X=1)=1/8; P(X≤2)=0+1/8+1/2=5/8; P(X≥2)=1/2+1/4+1/8=7/8.
The required constant is1/8 and the probabilities are1/8,5/8,7/8.

📋 CBSE Stepwise Marking Scheme

[0.5 marks] The masses for X=0,1,2,3,4 are 0,k,4k,2k,k; their sum 8k must equal1.
[1 mark] Thus k=1/8 and the distribution is (0,1/8,1/2,1/4,1/8).
[1 mark] P(X=1)=1/8; P(X≤2)=0+1/8+1/2=5/8; P(X≥2)=1/2+1/4+1/8=7/8.
[0.5 marks] The required constant is1/8 and the probabilities are1/8,5/8,7/8.

Master Chapter 13: Probability

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Probability.

📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →

← Previous Question

X=0,1,2,3,4,5,6 has probabilities C,2C,2C,3C,C²,2C²,7C²+C. Find C…

Next Question →

A group has50 scouts,30 trained in first aid and20 not. Select2…

Class 12 Maths · Probability · Long Answer #110

✅ Step-by-Step Solution

📋 CBSE Stepwise Marking Scheme

Master Chapter 13: Probability

More Practice Questions in Probability

Related Questions in Probability