CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 · Q232 Markssampling_without_replacement
CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 · Question 23 (Probability)
Two cards are drawn uniformly without replacement from cards numbered 1 through 22. Find the probability that both numbers are even. OR If \(P(A)=3/8\), \(P(B)=1/2\), \(P(A\cap B)=1/4\), find \(P(A^c\mid B^c)\).
Alternative 1 2 Marks
Two cards are drawn uniformly without replacement from cards numbered 1 through 22. Find the probability that both numbers are even.
Answer: 5/21
- There are 11 even cards among 22.
- The favourable unordered pairs number C(11,2)=55, while the total is C(22,2)=231.
- Their ratio is 55/231=5/21.
Alternative 2 2 Marks
If \(P(A)=3/8\), \(P(B)=1/2\), \(P(A\cap B)=1/4\), find \(P(A^c\mid B^c)\).
Answer: 3/4
- Use P(A′∩B′)=1−P(A∪B).
- The union has probability 3/8+1/2−1/4=5/8, so the numerator is 3/8 and P(B′)=1/2.
- Divide to get 3/4.