ProbabilityPYQ Sept 25Question 4483 of 187
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Three components A, B and C are manufactured separately and then assembled into a finished product. While producing the three components, it is found that 5 percent of component A, 4 percent of component B and 1 percent of component C are defective. What is the probability that the assembled product is free from defects?

Options

A0.75
B0.8
C0.85
D0.9
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Correct Answer

✅ Option d — 0.9

All Options:

  • A0.75
  • B0.8
  • C0.85
  • D0.9

Detailed Solution & Explanation

Let DA,DB,\displaystyle D_A, D_B, and DC\displaystyle D_C be the events that components A, B, and C are defective, respectively. We are given:
P(DA)=0.05,P(DB)=0.04,P(DC)=0.01P(D_A) = 0.05, \quad P(D_B) = 0.04, \quad P(D_C) = 0.01
1. **Find the probability that each component is non-defective (free from defects)**:
P(DA′)=1−P(DA)=1−0.05=0.95P(D_A') = 1 - P(D_A) = 1 - 0.05 = 0.95
P(DB′)=1−P(DB)=1−0.04=0.96P(D_B') = 1 - P(D_B) = 1 - 0.04 = 0.96
P(DC′)=1−P(DC)=1−0.01=0.99P(D_C') = 1 - P(D_C) = 1 - 0.01 = 0.99
2. **Find the probability that the assembled product is free from defects**:
Since the three components are manufactured separately, the events of them being defective or non-defective are independent. Therefore:
P(Product free from defects)=P(DA′∩DB′∩DC′)=P(DA′)×P(DB′)×P(DC′)P(\text{Product free from defects}) = P(D_A' \cap D_B' \cap D_C') = P(D_A') \times P(D_B') \times P(D_C')
P(Product free from defects)=0.95×0.96×0.99P(\text{Product free from defects}) = 0.95 \times 0.96 \times 0.99
P(Product free from defects)=0.912×0.99=0.90288P(\text{Product free from defects}) = 0.912 \times 0.99 = 0.90288
Rounding to the nearest option, we get 0.9\displaystyle 0.9.
Hence, **Option D** is the correct answer.

About This Chapter: Probability

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Probability Operations, Expected Value

A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.

View Official ICAI Syllabus

Exam Strategy Tip

Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.

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