Class CBSE Class 12 Mathematics Probability Q #973

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A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances of their manufacturing a defective smartphone are only 5%, 4% and 2% respectively. In his inventory he has 25% smartphones from company A, 35% smartphones from company B and 40% smartphones from company C.
COMPETENCY BASED
APPLY
4 Marks 2025 AISSCE(Board Exam) SUBJECTIVE
A person buys a smartphone from this shop.
(i) Find the probability that it was defective.
(ii) What is the probability that this defective smartphone was manufactured by company B ?
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Step-by-Step Solution

(i) Probability that the smartphone was defective:

Let D be the event that the smartphone is defective.

P(A) = 0.25, P(B) = 0.35, P(C) = 0.40

P(D|A) = 0.05, P(D|B) = 0.04, P(D|C) = 0.02

Using the law of total probability:

P(D) = P(A) * P(D|A) + P(B) * P(D|B) + P(C) * P(D|C)

P(D) = (0.25 * 0.05) + (0.35 * 0.04) + (0.40 * 0.02)

P(D) = 0.0125 + 0.014 + 0.008

P(D) = 0.0345

(ii) Probability that the defective smartphone was manufactured by company B:

We need to find P(B|D), which is the probability that the smartphone was manufactured by company B given that it is defective.

Using Bayes' theorem:

P(B|D) = [P(D|B) * P(B)] / P(D)

P(B|D) = (0.04 * 0.35) / 0.0345

P(B|D) = 0.014 / 0.0345

P(B|D) = 0.4058 (approximately)

Correct Answer: (i) 0.0345, (ii) 0.4058

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to apply the concepts of probability, specifically Bayes' theorem and the law of total probability, to solve a real-world problem.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a series of steps involving probability calculations, including applying Bayes' theorem and the law of total probability. These are specific procedures for solving probability problems.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. The question is designed to assess the student's ability to apply their knowledge of probability to a real-world scenario, rather than simply recalling definitions or formulas. It requires application of Bayes' theorem in a practical context.

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