CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Q273 Marksconditional_probability
CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Question 27 (Probability)
A fair die is rolled. Let A={1,2,5}, B={3,5}, C={2,3,4,5}. Find P(A | C), P(C | A), P(A∩B | C) and P(A∪B | C). OR Draw two cards independently with replacement from {1,2,3,4,5,6}. A is sum 10; B is first card other than 4. Find P(A∩B) and test independence.
Alternative 1 3 Marks
A fair die is rolled. Let A={1,2,5}, B={3,5}, C={2,3,4,5}. Find P(A | C), P(C | A), P(A∩B | C) and P(A∪B | C).
Answer: 1/2, 2/3, 1/4 and 3/4 respectively.
- A∩C={2,5}, giving 2/4 and 2/3 for the first two probabilities.
- A∩B∩C={5}, giving 1/4.
- (A∪B)∩C={2,3,5}, giving 3/4.
Alternative 2 3 Marks
Draw two cards independently with replacement from {1,2,3,4,5,6}. A is sum 10; B is first card other than 4. Find P(A∩B) and test independence.
Answer: P(A∩B)=1/18. The events are dependent.
- The ordered pairs for A are (4,6),(5,5),(6,4). Two satisfy B, giving 2/36.
- P(A)=3/36 and P(B)=5/6, so P(A)P(B)=5/72.
- Since 1/18=4/72 differs from 5/72, they are dependent.