CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Q374 Marksbayes_theorem
CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Question 37 (Probability)
In a survey, vaccine shares for A₁,A₂,A₃ were 25%,35%,40%, respectively. Their conditional protection probabilities in the question’s model were 60%,55%,50%.
Part (1) 1 Marks
Find the probability of infection given A₂.
Answer: 0.45.
- The protection probability given A₂ is 0.55.
- Take its complement to get 0.45.
Part (2) 1 Marks
Find the overall probability of protection.
Answer: 0.5425.
- Weight the three conditional probabilities by their vaccine shares.
- The sum 0.25·0.60+0.35·0.55+0.40·0.50 equals 0.5425.
Part (3) 2 Marks
Given infection, find the probability the person received A₁.
Answer: 40/183.
- The joint probability of A₁ and infection is 0.25·0.40=0.10.
- The overall infection probability is 1−0.5425=0.4575.
- Divide 0.10 by 0.4575 to get 40/183.
Part (4) 2 Marks
Given protection, find the probability the person received A₃.
Answer: 80/217.
- The joint probability of A₃ and protection is 0.40·0.50=0.20.
- The overall protection probability is 0.5425.
- Divide 0.20 by 0.5425 to get 80/217.