ProbabilityMCQMTP June 2023 Series IQuestion 3361 of 187
All Questions

If a number is selected at random from the first 50\displaystyle 50 natural numbers, what will be the probability that the selected no. is a multiple of 3\displaystyle 3 and 4\displaystyle 4?

Options

A5/50\displaystyle 5/50
B4/25\displaystyle 4/25
C3/50\displaystyle 3/50
D4/25\displaystyle 4/25
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Correct Answer

✅ Option b — 4/25\displaystyle 4/25

All Options:

  • A5/50\displaystyle 5/50
  • B4/25\displaystyle 4/25
  • C3/50\displaystyle 3/50
  • D4/25\displaystyle 4/25

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Detailed Solution & Explanation

**Probability of Selecting a Multiple of 3 and 4** Total natural numbers = 50 (from 1 to 50) A number is a multiple of both 3 and 4 if and only if it is a multiple of their least common multiple (LCM), which is 12. Let's list the multiples of 12 in the range from 1 to 50: 12,24,36,4812, 24, 36, 48 So, the number of favorable outcomes is 4. The probability of selecting such a number is: P=450=225P = \frac{4}{50} = \frac{2}{25} Note: Option B is misprinted in the question paper as 4/25\displaystyle 4/25 instead of 2/25\displaystyle 2/25 (which was the correct value of Option B in previous exam series). We point out this typographical error. 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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