Q695: If E and F are two independent events such that \( P(E) = \f...

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} $

(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:$$P(E \mid \overline{F}) = \frac{2}{3}$$

AI Tutor Explanation

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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MCQ_SINGLE

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SUBJECTIVE

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