Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Probability · Long Answer3 Marksprobability_distributions

Class 12 Maths · Probability · Long Answer #65

Roll two independent fair dice. Let X be the absolute difference of their scores. Find its distribution.

✅ Step-by-Step Solution

Final Answer: P(X=0)=1/6; P(X=1)=5/18; P(X=2)=2/9; P(X=3)=1/6; P(X=4)=1/9; P(X=5)=1/18.
  1. There are 36 equally likely ordered dice outcomes; X ranges from 0 to 5.
  2. For X=0 there are 6 doubles. For a positive difference d, there are 2(6−d) ordered pairs, giving counts 10,8,6,4,2. The probabilities are P(X=0)=1/6; P(X=1)=5/18; P(X=2)=2/9; P(X=3)=1/6; P(X=4)=1/9; P(X=5)=1/18. Their sum is 1.
  3. All masses are nonnegative and exhaust the possible values of X.
  4. P(X=0)=1/6; P(X=1)=5/18; P(X=2)=2/9; P(X=3)=1/6; P(X=4)=1/9; P(X=5)=1/18.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] There are 36 equally likely ordered dice outcomes; X ranges from 0 to 5.
  • [1 mark] For X=0 there are 6 doubles. For a positive difference d, there are 2(6−d) ordered pairs, giving counts 10,8,6,4,2. The probabilities are P(X=0)=1/6; P(X=1)=5/18; P(X=2)=2/9; P(X=3)=1/6; P(X=4)=1/9; P(X=5)=1/18. Their sum is 1.
  • [1 mark] All masses are nonnegative and exhaust the possible values of X.
  • [0.5 marks] P(X=0)=1/6; P(X=1)=5/18; P(X=2)=2/9; P(X=3)=1/6; P(X=4)=1/9; P(X=5)=1/18.

Master Chapter 13: Probability

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Probability.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
Draw twice independently with replacement from an urn with equal…
Next Question →
Select 3 distinct numbers uniformly from {1,2,3,4,5,6}. X is their…

More Practice Questions in Probability

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

Related Questions in Probability

Class 12 Probability · Mcq Single Correct
Given P(A)=4/5 and P(A∩B)=7/10, find P(B|A).
Class 12 Probability · Mcq Single Correct
Five independent fair coins are tossed. Find the probability of at least one head.
Class 12 Probability · Mcq Single Correct
Given P(A|B)=0.3, P(A)=0.4, P(B)=0.8, find P(B|A).
Class 12 Probability · Mcq Single Correct
Two independent fair dice have sum 9. Find the conditional probability that at least one die…
Class 12 Probability · Mcq Single Correct
Choose an ordered pair (a,b) uniformly with distinct a,b from {1,2,3,4,5}. Find P(a/b is an…
Class 12 Probability · Mcq Single Correct
Given P(A)=0.4, P(B)=0.3 and P(A∪B)=0.5, find P(B′∩A).