CBSE Class 12 Mathematics 2026: question 31(a)

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. (i) $A\cap C=\{2,5\}$ and $n(C)=4$, so $P(A|C)=\frac{n(A\cap C)}{n(C)}=\frac{2}{4}=\frac{1}{2}$

   1 mark

2. (i) $n(A)=3$, so $P(C|A)=\frac{n(C\cap A)}{n(A)}=\frac{2}{3}$

   ½ mark

3. (ii) $A\cap B=\{5\}$ and $(A\cap B)\cap C=\{5\}$, so $P(A\cap B|C)=\frac{1}{4}$

   1 mark

4. (ii) $A\cup B=\{1,2,3,5\}$ and $(A\cup B)\cap C=\{2,3,5\}$, so $P(A\cup B|C)=\frac{3}{4}$

   ½ mark

Answer: (i) $P(A|C)=\frac{1}{2}$, $P(C|A)=\frac{2}{3}$; (ii) $P(A\cap B|C)=\frac{1}{4}$, $P(A\cup B|C)=\frac{3}{4}$

Revise the chapter

• Chapter: Probability (notes, formulas, where marks are lost and every past question)
• Topic: Conditional Probability