CBSE Class 12 Mathematics 2026 Main Paper 65/2/2 · Q384 Marksbayes_theorem
CBSE Class 12 Mathematics 2026 Main Paper 65/2/2 · Question 38 (Probability)
In a group of 50 smokers, 30 are male. Lung complications occur in 170 per 1000 male smokers and 120 per 1000 female smokers in the model. Select one person uniformly and test for lung complications.
Part (1) 1 Marks
Find the probability that the selected person is female.
Answer: 2/5.
- There are 50−30=20 female smokers.
- Divide by the group size: 20/50=2/5.
Part (2) 1 Marks
Given that the selected person is male, find the probability of no lung complications.
Answer: 83/100.
- Use the conditional male complication probability 170/1000.
- Its complement is 1−170/1000=83/100.
Part (3) 2 Marks
Given that the selected person has lung complications, find the probability that the person is female.
Answer: 8/25.
- The female and male prior probabilities are 2/5 and 3/5.
- The female-and-complications probability is (2/5)(0.12)=0.048. The total complication probability is 0.048+(3/5)(0.17)=0.15.
- Bayes’ rule gives 0.048/0.15=8/25.
Part (4) 2 Marks
Given that the selected person has no lung complications, find the probability that the person is male.
Answer: 249/425.
- The no-complications probabilities for male and female smokers are 0.83 and 0.88.
- The male-and-no-complications probability is 0.498. The total no-complications probability is 0.498+0.352=0.85.
- Bayes’ rule gives 0.498/0.85=249/425.