ProbabilityMCQPYQ Dec 22Question 3287 of 187
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If a number is selected at random from the first 50\displaystyle 50 natural numbers, what will be the probability that the selected number is a multiple of 3\displaystyle 3 and 4\displaystyle 4?

Options

A550\displaystyle \frac{5}{50}
B225\displaystyle \frac{2}{25}
C330\displaystyle \frac{3}{30}
D425\displaystyle \frac{4}{25}
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Correct Answer

✅ Option b — 225\displaystyle \frac{2}{25}

All Options:

  • A550\displaystyle \frac{5}{50}
  • B225\displaystyle \frac{2}{25}
  • C330\displaystyle \frac{3}{30}
  • D425\displaystyle \frac{4}{25}

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Detailed Solution & Explanation

**Multiple of Both 3 and 4 (i.e., multiple of LCM(3,4) = 12)** First 50 natural numbers: 1 to 50. A number that is a multiple of both 3 and 4 must be a multiple of LCM(3,4)=12\displaystyle \text{LCM}(3,4) = 12. Multiples of 12 in first 50 natural numbers: - 12,24,36,48\displaystyle 12, 24, 36, 48 → **4 numbers** P=450=225P = \frac{4}{50} = \frac{2}{25} Hence, **Option B** 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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