Class 12 Probability · Long Answer3 Marksprobability_distributions
Class 12 Maths · Probability · Long Answer #109
X=0,1,2,3,4,5,6 has probabilities C,2C,2C,3C,C²,2C²,7C²+C. Find C and E(X).
✅ Step-by-Step Solution
Final Answer: C=1/10; E(X)=133/50=2.66
- Normalization gives 10C²+9C=1, or (10C−1)(C+1)=0.
- C=−1 gives negative probability P(X=0), so C=1/10 is the valid root.
- E(X)=0·C+1·2C+2·2C+3·3C+4C²+5·2C²+6(7C²+C)=21C+56C². Substitute C=1/10 to get 2.1+0.56=2.66.
- Thus C=1/10 and E(X)=133/50=2.66.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Normalization gives 10C²+9C=1, or (10C−1)(C+1)=0.
- [1 mark] C=−1 gives negative probability P(X=0), so C=1/10 is the valid root.
- [1 mark] E(X)=0·C+1·2C+2·2C+3·3C+4C²+5·2C²+6(7C²+C)=21C+56C². Substitute C=1/10 to get 2.1+0.56=2.66.
- [0.5 marks] Thus C=1/10 and E(X)=133/50=2.66.
Master Chapter 13: Probability
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Probability.
← Previous Question
A box has20 pens,2 defective. Draw5 independently with replacement…
Next Question →X is the number of colleges granting admission to an applicant. Its…
More Practice Questions in Probability
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).