Class CBSE Class 12 Mathematics Probability Q #695
KNOWLEDGE BASED
APPLY
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
If E and F are two independent events such that \( P(E) = \frac{2}{3} \), \( P(F) = \frac{3}{7} \), then \(\mathbf{P(E \mid \overline{F})}\) is equal to:
(A) \( \frac{1}{6} \)
(B) \( \frac{1}{2} \)
(C) \( \frac{2}{3} \)
(D) \( \frac{7}{9} \)
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Correct Answer: C
Explanation
If events $E$ and $F$ are independent, then $$\mathbf{P(E \mid F) = P(E)}$$And similarly, if $E$ and $F$ are independent, then $E$ and $\overline{F}$ are also independent:$$\mathbf{P(E \mid \overline{F}) = P(E)}$$ Substitute the Given ValueSince $E$ and $F$ are independent events, we can directly state the result:$$P(E \mid \overline{F}) = P(E)$$Given that $P(E) = \frac{2}{3}$, we have:$$P(E \mid \overline{F}) = \frac{2}{3}$$

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Step-by-Step Solution

Since E and F are independent events, E and \(\overline{F}\) are also independent events.

Therefore, \(P(E \mid \overline{F}) = P(E)\)

Given \(P(E) = \frac{2}{3}\)

Thus, \(P(E \mid \overline{F}) = \frac{2}{3}\)

Correct Answer: \( \frac{2}{3} \)

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires students to apply the concepts of independent events and conditional probability to calculate the desired probability.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of independent events and how it relates to conditional probability. It requires the student to know that if E and F are independent, then E and the complement of F are also independent.
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 textbook concepts related to probability and independent events.

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