Class CBSE Class 12 Mathematics Probability Q #1435
KNOWLEDGE BASED
REMEMBER
3 Marks 2025 AISSCE(Board Exam) 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.
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Detailed Solution

Step 1: Define Events

Let A be the event that the student buys a colouring book, and B be the event that the student buys a box of colours.

Step 2: Write Down Given Probabilities

We are given: $P(A) = 0.7$ $P(B) = 0.2$ $P(A|B) = 0.3$

Step 3: Find P(A and B)

We know that $P(A|B) = \frac{P(A \cap B)}{P(B)}$. Therefore, $P(A \cap B) = P(A|B) \times P(B) = 0.3 \times 0.2 = 0.06$ So, the probability that the student buys both the colouring book and the box of colours is 0.06.

Step 4: Find P(B|A)

We need to find $P(B|A)$, which is the probability that the student buys a box of colours given that she buys the colouring book. $P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.7} = \frac{6}{70} = \frac{3}{35}$ So, the probability that the student buys a box of colours given that she buys the colouring book is $\frac{3}{35}$.

Final Answer: (i) 0.06, (ii) 3/35

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Pedagogical Audit
Bloom's Analysis: This is an REMEMBER question because it requires recalling the formula for conditional probability and applying it directly to the given values.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of conditional probability and its application in a straightforward scenario. It involves understanding the relationship between events and probabilities.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. It directly assesses the student's understanding and application of the conditional probability formula, a core concept in the probability chapter.

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