CUET · MATHS · PYQ PAPER 2025

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{2}, P(B)=\frac{1}{3}, P(B \mid A)=\frac{1}{4}\), then \(P(A \mid B)\) is :

A \(\frac{1}{8}\)
B \(\frac{7}{8}\)
C \(\frac{3}{8}\)
D \(\frac{5}{8}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{3}{8}\)

Step-by-step Solution

Detailed explanation

\(P(A \cap B) = P(B \mid A) \cdot P(A)\) \(P(A \cap B) = \frac{1}{4} \cdot \frac{1}{2} = \frac{1}{8}\) \(P(A \mid B) = \frac{P(A \cap B)}{P(B)}\) \(P(A \mid B) = \frac{\frac{1}{8}}{\frac{1}{3}} = \frac{3}{8}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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From CUET

Match List-l with List-II

List-l (Solutions)	List-II (Explanation)
(A) Saturated solution	(I) Solution having two components.
(B) Isotonic solutions	(II) A solution whose osmotic pressure is more than that of another.
(C) Binary solution	(III) A solution which contains the maximum amount of solute that can be dissolved in a given amount of solvent at a given temperature.
(D) Hypertonic solution	(IV) The solutions having same osmotic pressure at a given temperature.

Choose the correct answer from the options given below :

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