ProbabilityMCQMTP June 2023 Series IIQuestion 2827 of 295
All Questions

A machine is made of two parts A and B. The manufacturing process of each part is such that probability of defective in part A is 0.08\displaystyle 0.08 and that B is 0.05\displaystyle 0.05. What is the probability that the assembled part will not have any defect?

Options

A0.934\displaystyle 0.934
B0.864\displaystyle 0.864
C0.85\displaystyle 0.85
D0.874\displaystyle 0.874
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Correct Answer

✅ Option d — 0.874\displaystyle 0.874

All Options:

  • A0.934\displaystyle 0.934
  • B0.864\displaystyle 0.864
  • C0.85\displaystyle 0.85
  • D0.874\displaystyle 0.874

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Detailed Solution & Explanation

Let DA\displaystyle D_A and DB\displaystyle D_B represent the events that part A and part B are defective, respectively. 1. We are given the following defect probabilities: - P(DA)=0.08\displaystyle P(D_A) = 0.08 - P(DB)=0.05\displaystyle P(D_B) = 0.05 2. The probabilities that parts A and B are not defective are: - P(DA′)=1−0.08=0.92\displaystyle P(D_A') = 1 - 0.08 = 0.92 - P(DB′)=1−0.05=0.95\displaystyle P(D_B') = 1 - 0.05 = 0.95 3. Assuming the manufacturing processes of the two parts are independent, the probability that the assembled part has no defect (both parts are non-defective) is: P(No defect)=P(DA′)×P(DB′)=0.92×0.95=0.874P(\text{No defect}) = P(D_A') \times P(D_B') = 0.92 \times 0.95 = 0.874 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.

Key Concepts to Understand

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

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