CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 · Q374 Markscase_study
CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 · Question 37 (Probability)
Companies X,Y,Z have selection probabilities 1/3,2/9,4/9. Their conditional probabilities of poor construction quality are 20%,40%,30%, respectively. Answer both parts.
Part (1) 2 Marks
Given strong construction, find the probability the selected company was X.
Answer: 3/8
- Strong-construction likelihoods for X,Y,Z are 4/5,3/5,7/10.
- The joint masses are 4/15,2/15,14/45, with total 32/45.
- Divide (4/15)/(32/45)=3/8.
Part (2) 2 Marks
Given that part of the newly constructed building falls off, find the probability the selected company was Y or Z.
Answer: 10/13 under the intended identification with poor quality.
- Interpret the observation as the poor-quality event used by the probability model.
- The joint masses of poor quality from X,Y,Z are 1/15,4/45,2/15. Their total is 13/45 and the Y-or-Z portion is 10/45.
- The conditional probability is (10/45)/(13/45)=10/13.