Class 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
Prev Next
Correct Answer: D

AI Tutor Explanation

Powered by Gemini

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

AI generated content. Review strictly for academic accuracy.

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.

More from this Chapter

SA
Find the probability distribution of the number of boys in families having three children, assuming equal probability for a boy and a girl.
SA
31. From a lot of 30 bulbs which include 6 defective bulbs, a sample of 2 bulbs is drawn at random one by one with replacement. Find the probability distribution of the number of defective bulbs and hence find the mean number of defective bulbs.
LA
(a) In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/5 be the probability that he knows the answer and 2/5 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/3. What is the probability that the student knows the answer, given that he answered it correctly? OR (b) A box contains 10 tickets, 2 of which carry a prize of ₹8 each, 5 of which carry a prize of ₹4 each, and remaining 3 carry a prize of ₹2 each. If one ticket is drawn at random, find the mean value of the prize.
SA
E and F are two independent events such that $P(\overline{E})=0\cdot6$ and $P(E\cup F)=0\cdot6$ Find $P(F)$ and $P(\overline{E}\cup\overline{F})$
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.
View All Questions