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) \( \frac{7}{9} \)
Prev Next
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

Powered by Gemini

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

AI generated content. Review strictly for academic accuracy.

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.

More from this Chapter

SA
A survey was conducted on the patients who have undergone knee replacement surgeries. It was found that, Robotic Knee replacement surgeries have 90% success rate. On a particular day, robotic surgery was performed on three patients, A, B and C, one after the other. Assuming that the success and failure of each surgery is independent of each other, find the probability that: (i) exactly one surgery is successful, (ii) at most two surgeries are successful.
SA
A pair of dice is thrown simultaneously. If $X$ denotes the absolute difference of numbers obtained on the pair of dice, then find the probability distribution of $X$.
ASSERTION_REASON
In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is $\frac{2}{3}$.
SA
The chances of P, Q and R getting selected as CEO of a company are in the ratio 4: 1: 2 respectively. The probabilities for the company to increase its profits from the previous year under the new CEO, P, Q or R are 0-3, 0-8 and 0.5 respectively. If the company increased the profits from the previous year, find the probability that it is due to the appointment of R as CEO.
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).
View All Questions