CBSE Class 12 Mathematics Probability Q #1838
COMPETENCY BASED
EVALUATE
1 Marks 2026 AISSCE(Board Exam) ASSERTION REASON
Assertion: In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is $\frac{2}{3}$.
Reason: For any two events A and B, $P(A|B) = \frac{P(A \cup B)}{P(B)}$
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is NOT the correct explanation of A.
(C) A is true but R is false.
(D) A is false but R is true.
Prev Finish
Correct Answer: C

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Detailed Solution

Step 1: Define the Sample Space and Events

The sample space for an unbiased die is $S = \{1, 2, 3, 4, 5, 6\}$. Let event $A$ be getting a prime number, so $A = \{2, 3, 5\}$. Let event $B$ be getting an odd number, so $B = \{1, 3, 5\}$.

Step 2: Calculate Probabilities

The probability of event $B$ is $P(B) = \frac{3}{6} = \frac{1}{2}$. The intersection $A \cap B$ (prime and odd) is $\{3, 5\}$, so $P(A \cap B) = \frac{2}{6} = \frac{1}{3}$.

Step 3: Evaluate the Assertion

The conditional probability is $P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{1/3}{1/2} = \frac{2}{3}$. Thus, the Assertion is True.

Step 4: Evaluate the Reason

The provided formula in the context is $P(A|B) = \frac{P(A \cup B)}{P(B)}$. This is mathematically incorrect. The correct definition of conditional probability is $P(A|B) = \frac{P(A \cap B)}{P(B)}$. Thus, the Reason is False.

Final Answer: Assertion is True, but Reason is False.

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Pedagogical Audit
Bloom's Analysis: This is an EVALUATE question because the student must verify the validity of a mathematical statement and identify the error in a provided definition.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the fundamental definition of conditional probability and the ability to distinguish between intersection and union in probability theory.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. It requires the student to apply the formula for conditional probability while critically analyzing the provided context for conceptual accuracy.
||KEY:C

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