CBSE Class 12 Mathematics 2026 Main Paper 65/3/1 · Q374 Marksbayes_theorem
CBSE Class 12 Mathematics 2026 Main Paper 65/3/1 · Question 37 (Probability)
In an entrance examination, 40% of candidates took a gap year after Class 12 and the others were regular students. Of those who took a gap year, 5% qualified. Among regular students, 10% qualified.
Part (1) 1 Marks
What is the probability a random candidate is a regular student?
Answer: 3/5.
- The gap-year group has probability 0.40.
- Its complement is 0.60=3/5.
Part (2) 1 Marks
What is the probability a randomly selected gap-year candidate does not qualify?
Answer: 19/20.
- Within the gap-year group the qualification probability is 0.05.
- Its complement is 0.95=19/20.
Part (3) 2 Marks
A randomly selected candidate qualified. Find the probability they are a regular student.
Answer: 3/4.
- The regular-and-qualified probability is 0.60·0.10=0.06.
- The total qualified probability is 0.06+0.40·0.05=0.08.
- Conditioning gives 0.06/0.08=3/4.
Part (4) 2 Marks
A randomly selected candidate did not qualify. Find the probability they are a regular student.
Answer: 27/46.
- The regular-and-not-qualified probability is 0.60·0.90=0.54.
- The total not-qualified probability is 0.54+0.40·0.95=0.92.
- Conditioning gives 0.54/0.92=27/46.