For any two events A and B, if P(A)=1/2, P(B)=2/3 and P(A B)=1/4, then P(A/B) equals: (A) 3/8 (B) 8/9 (C) 5/8 (D) 1/4

MathsCBSE Class 12 · Sample paper, session 2024-25 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2024-25: question 8

From the official CBSE sample question paper for 2024-25, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQProbability

For any two events $A$ and $B$ , if $P (\overline{A}) = \frac{1}{2}$ , $P (\overline{B}) = \frac{2}{3}$ and $P (A \cap B) = \frac{1}{4}$ , then $P (\overset{ˉ}{A} / \overset{ˉ}{B})$ equals:

(A) $\frac{3}{8}$
(B) $\frac{8}{9}$
(C) $\frac{5}{8}$
(D) $\frac{1}{4}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

$\overset{ˉ}{A} \cap \overset{ˉ}{B}$ is the complement of $A \cup B$ .

Hint 2

Find $P (A \cup B)$ by addition theorem.

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.

$P (A) = \frac{1}{2}, P (B) = \frac{1}{3}$ , $P (A \cup B) = \frac{1}{2} + \frac{1}{3} - \frac{1}{4} = \frac{7}{12}$ .
$P (\overset{ˉ}{A} / \overset{ˉ}{B}) = \frac{1 - P ( A \cup B )}{P ( B ˉ )} = \frac{5/12}{2/3} = \frac{5}{8}$ . Option (C).
1 mark

Answer: $\frac{5}{8}$ , option (C)

Where the marks are

Uses $P (\overset{ˉ}{A} \cap \overset{ˉ}{B}) = 1 - P (A \cup B)$ to get $5/8$ (1 mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Probability, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2024-25: every question, by section.

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CBSE Class 12 Mathematics sample paper 2024-25: question 8

Hints

Step-by-step solution

Revise the chapter

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