CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Q384 Markstotal_probability
CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Question 38 (Probability)
Bag I contains 5 red and 6 black balls. Bag II contains 3 red and 4 black balls. All specified draws and transfers are uniform.
Part (1) 1 Marks
Draw one ball from each bag. Find the probability both are red.
Answer: 15/77.
- The red probabilities are 5/11 and 3/7.
- Multiply to obtain 15/77.
Part (2) 1 Marks
Draw one ball from each bag. Find the probability of one red and one black.
Answer: 38/77.
- The two disjoint color orders have probabilities (5/11)(4/7) and (6/11)(3/7).
- Add them to obtain 38/77.
Part (3) 2 Marks
Transfer one ball from I to II, then draw from II. Find the red probability.
Answer: 19/44.
- The transfer is red with probability 5/11 and black with probability 6/11.
- After the transfer the red probability in II is respectively 4/8 or 3/8.
- Weight to get (5·4+6·3)/88=19/44.
Part (4) 2 Marks
After the same transfer procedure, find the black probability.
Answer: 25/44.
- The two conditional black probabilities in II are 4/8 and 5/8.
- Weight them by the transfer probabilities 5/11 and 6/11.
- The total is (5·4+6·5)/88=25/44.