CBSE Class 12 Mathematics Probability Q #693
KNOWLEDGE BASED
APPLY
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
If \(P(A\cup B)=0.9\) and \(P(A\cap B)=0\cdot4,\) then \(P(\overline{A})+P(\overline{B})\) is:
(A) 0.3
(B) 1
(C) 1.3
(D) 0.7
Prev Next
Correct Answer: D

AI Tutor Explanation

Powered by Gemini

Step-by-Step Solution

We are given \(P(A\cup B)=0.9\) and \(P(A\cap B)=0.4\). We need to find \(P(\overline{A})+P(\overline{B})\).

We know that \(P(A\cup B) = P(A) + P(B) - P(A\cap B)\).

So, \(0.9 = P(A) + P(B) - 0.4\).

Therefore, \(P(A) + P(B) = 0.9 + 0.4 = 1.3\).

We also know that \(P(\overline{A}) = 1 - P(A)\) and \(P(\overline{B}) = 1 - P(B)\).

So, \(P(\overline{A}) + P(\overline{B}) = (1 - P(A)) + (1 - P(B)) = 2 - (P(A) + P(B))\).

Substituting the value of \(P(A) + P(B)\), we get:

\(P(\overline{A}) + P(\overline{B}) = 2 - 1.3 = 0.7\).

Correct Answer: 0.7

AI Suggestion: Option D

AI generated content. Review strictly for academic accuracy.

Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the formulas of probability and set theory to find the value of the given expression.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding of the concepts of union, intersection, and complements of events in probability. The student needs to know the formulas related to these concepts to solve the problem.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of probability formulas as covered in the textbook.

More from this Chapter

SA
A box contains 6 cards numbered 1 to 6. A student is asked to pick up two cards, one by one after replacement and note down the numbers on the cards. Let A be the event of getting sum of the numbers on two cards as 10, and B, the event of a number other than 4 on the first card selected. Find P(A and B) and find whether the events A and B are independent events or not.
SA
In a school, the probability of holding a debate competition is $\frac{1}{3}$ and that of a quiz competition is $\frac{2}{3}$. In the two participating teams, A has 4 girls and 6 boys and B has 7 girls and 3 boys. If a debate competition is held, the students are selected from team A and for the quiz competition they are selected from team B. If only two students are to be chosen from the teams, then find the probability that one will be a girl and the other a boy.
SA
The probability that a student buys a colouring book is 0.7 and that she buys a box of colours is 0.2. The probability that she buys a colouring book, given that she buys a box of colours, is 0.3. Find the probability that the student: (i) Buys both the colouring book and the box of colours. (ii) Buys a box of colours given that she buys the colouring book.
SA
A coin is tossed twice. Let X be a random variable defined as number of heads minus number of tails. Obtain the probability distribution of X and also find its mean.
MCQ_SINGLE
Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is
View All Questions