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

SA
A person has a fruit box that contains 6 apples and 4 oranges. He picks out a fruit three times, one after the other, after replacing the previous one in the box. Find: (i) The probability distribution of the number of oranges he draws. (ii) The expectation of the random variable (number of oranges).
SUBJECTIVE
A person buys a smartphone from this shop. (i) Find the probability that it was defective. (ii) What is the probability that this defective smartphone was manufactured by company B ?
SA
The probability of simultaneous occurrence of at least one of the two events $X$ and$Y$ is $a$. If the probability that exactly one of the events $X, Y$ occurs is $b$, prove that $P(X') + P(Y') = 2 – 2a + b$.
SA
For the vacancy advertised in the newspaper, 3000 candidates submitted their applications. From the data it was revealed that two third of the total applicants were females and other were males. The selection for the job was done through a written test. The performance of the applicants indicates that the probability of a male getting a distinction in written test is 0.4 and that a female getting a distinction is 0.35. Find the probability that the candidate chosen at random will have a distinction in the written test.
SA
The probability distribution for the number of students being absent in a class on a Saturday is as follows: X: 0, 2, 4, 5; $P(X)$: p, 2p, 3p, p. Where X is the number of students absent. (i) Calculate p. (ii) Calculate the mean of the number of absent students on Saturday.
View All Questions