CBSE Class 12 Mathematics 2026 Main Paper 65/4/3 · Q374 Marksbayes_theorem
CBSE Class 12 Mathematics 2026 Main Paper 65/4/3 · Question 37 (Probability)
Box I contains 30 red caps, Box II contains 20 red and 10 green caps, and Box III contains 30 green caps. Box i is selected with probability i/6 for i=1,2,3, and then a cap is drawn uniformly from that box.
Part (1) 2 Marks
What is the probability the cap is red?
Answer: 7/18.
- The conditional probabilities of red are 1, 2/3 and 0 in the three boxes.
- Weight them by 1/6, 2/6 and 3/6, respectively.
- Their sum is 1/6+2/9=7/18.
Part (2) 2 Marks
Given a green cap was selected, what is the probability it came from Box II?
Answer: 2/11.
- The probability of green is 1−7/18=11/18.
- The joint probability of Box II and green is (2/6)(1/3)=1/9.
- Divide 1/9 by 11/18 to obtain 2/11.