ProbabilityMCQMTP Dec 22 - Series IQuestion 3358 of 187
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The odds in favor of event A\displaystyle A in a trial is 3:1\displaystyle 3:1. In three independent trials, the probability of non-occurrence of event A\displaystyle A is

Options

A1/64\displaystyle 1/64
B1/32\displaystyle 1/32
C1/27\displaystyle 1/27
D1/8\displaystyle 1/8
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Correct Answer

✅ Option a — 1/64\displaystyle 1/64

All Options:

  • A1/64\displaystyle 1/64
  • B1/32\displaystyle 1/32
  • C1/27\displaystyle 1/27
  • D1/8\displaystyle 1/8

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Detailed Solution & Explanation

**Probability of Non-Occurrence in Three Trials** Given: - Odds in favor of event A\displaystyle A are 3:1\displaystyle 3:1. **Step 1: Find the probability of occurrence and non-occurrence in a single trial** P(A)=33+1=34P(A) = \frac{3}{3+1} = \frac{3}{4} P(Aˉ)=1−P(A)=14P(\bar{A}) = 1 - P(A) = \frac{1}{4} **Step 2: Probability of non-occurrence in three independent trials** Since the trials are independent, the probability of non-occurrence in all three trials is the product of their individual probabilities: P(non-occurrence in 3 trials)=[P(Aˉ)]3=(14)3=164P(\text{non-occurrence in 3 trials}) = [P(\bar{A})]^3 = \left(\frac{1}{4}\right)^3 = \frac{1}{64} Hence, **Option A** 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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