Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Probability · Very Long Answer5 Marksprobability_distributions

Class 12 Maths · Probability · Very Long Answer #83

Ten tickets consist of two prizes of ₹8, five of ₹4, and three of ₹2. Draw one uniformly. Find the expected prize.

✅ Step-by-Step Solution

Final Answer: P(X=2)=3/10; P(X=4)=1/2; P(X=8)=1/5. Mean=21/5.
  1. Let X be the prize amount; possible values are ₹2,₹4,₹8.
  2. The category probabilities are the ticket counts divided by 10: 3/10,5/10,2/10.
  3. The resulting distribution is P(X=2)=3/10; P(X=4)=1/2; P(X=8)=1/5. Its nonnegative masses sum to 1.
  4. E(X)=ΣxP(X=x)=(2)(3/10)+(4)(1/2)+(8)(1/5)=21/5.
  5. P(X=2)=3/10; P(X=4)=1/2; P(X=8)=1/5. Mean=21/5.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Let X be the prize amount; possible values are ₹2,₹4,₹8.
  • [1 mark] The category probabilities are the ticket counts divided by 10: 3/10,5/10,2/10.
  • [1 mark] The resulting distribution is P(X=2)=3/10; P(X=4)=1/2; P(X=8)=1/5. Its nonnegative masses sum to 1.
  • [1 mark] E(X)=ΣxP(X=x)=(2)(3/10)+(4)(1/2)+(8)(1/5)=21/5.
  • [1 mark] P(X=2)=3/10; P(X=4)=1/2; P(X=8)=1/5. Mean=21/5.

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
An urn contains 4 white and 3 red balls. Draw three uniformly…
Next Question →
Select two distinct numbers uniformly from {1,2,3,4,5}. 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).