CBSE Class 12 Mathematics Probability Q #687
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2024 AISSCE(Board Exam) MCQ SINGLE
Let E and F be two events such that \(P(E)=0\cdot1\), \(P(F)=0\cdot3,\) \(P(E\cup F)=0\cdot4\) then \(P(F|E)\) is:
(A) 0.6
(B) 0.4
(C) 0.5
(D) 0
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Correct Answer: D

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Step-by-Step Solution

We are given \(P(E) = 0.1\), \(P(F) = 0.3\), and \(P(E \cup F) = 0.4\). We need to find \(P(F|E)\).

First, we use the formula for the probability of the union of two events:

\(P(E \cup F) = P(E) + P(F) - P(E \cap F)\)

Plugging in the given values:

\(0.4 = 0.1 + 0.3 - P(E \cap F)\)

Solving for \(P(E \cap F)\):

\(P(E \cap F) = 0.1 + 0.3 - 0.4 = 0\)

Now, we use the formula for conditional probability:

\(P(F|E) = \frac{P(E \cap F)}{P(E)}\)

Plugging in the values:

\(P(F|E) = \frac{0}{0.1} = 0\)

Correct Answer: 0

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires students to comprehend and apply the formula for conditional probability, given the probabilities of individual events and their union.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of conditional probability and how it relates to the probabilities of individual events and their union. It requires the student to know the formula and apply it correctly.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the student's understanding and application of a standard formula from the textbook regarding probability.

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