Class CBSE Class 12 Mathematics Probability Q #1739
COMPETENCY BASED
APPLY
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
For two events A and B such that $P(A) \ne 0$ and $P(B) \ne 1$, $P(A^{\prime}/B^{\prime})=$
(A) $1-P(A/B)$
(B) $1-P(A^{\prime}/B)$
(C) $\frac{1-P(A\cap B)}{P(B^{\prime})}$
(D) $\frac{1-P(A\cup B)}{P(B^{\prime})}$
Prev Next
Correct Answer: D

AI Tutor Explanation

Powered by Gemini

Detailed Solution

Step 1: Apply the definition of Conditional Probability

The conditional probability of an event $A'$ given $B'$ is defined as: $$P(A'/B') = \frac{P(A' \cap B')}{P(B')}$$

Step 2: Apply De Morgan's Law

According to De Morgan's Law, the intersection of the complements of two sets is the complement of their union: $$A' \cap B' = (A \cup B)'$$ Therefore, $P(A' \cap B') = P((A \cup B)') = 1 - P(A \cup B)$.

Step 3: Substitute and Simplify

Substitute the result from Step 2 into the formula from Step 1: $$P(A'/B') = \frac{1 - P(A \cup B)}{P(B')}$$

Final Answer: D

AI generated content. Review strictly for academic accuracy.

Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to synthesize the definition of conditional probability with set-theoretic identities (De Morgan's Law) to derive a specific expression.
Knowledge Dimension: PROCEDURAL
Justification: The student must follow a sequence of logical steps involving probability axioms and set operations to reach the correct algebraic form.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. This question tests the conceptual grasp of Probability (Chapter 13) beyond rote memorization, specifically focusing on the properties of complements and conditional events.

More from this Chapter

MCQ_SINGLE
Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is
MCQ_SINGLE
If E and F are two events such that \(P(E)>0\) and \(P(F)\ne1,\) then \(P(\overline{E}/\overline{F})\) is
SA
31. From a lot of 30 bulbs which include 6 defective bulbs, a sample of 2 bulbs is drawn at random one by one with replacement. Find the probability distribution of the number of defective bulbs and hence find the mean number of defective bulbs.
VSA
In a village of 8000 people, 3000 go out of the village to work and 4000 are women. It is noted that 30% of women go out of the village to work. What is the probability that a randomly chosen individual is either a woman or a person working outside the village?
MCQ_SINGLE
If $3P(A)=P(B)=\frac{3}{5}$ and $P(A|B)=\frac{2}{3}$ then $P(A\cup B)$ is:
View All Questions