ProbabilityMCQMTP Jun 23 - Series IIQuestion 3362 of 187
All Questions

A number is selected at random from first 70\displaystyle 70 natural numbers. What is the chance that it is a multiple of either 5\displaystyle 5 or 14\displaystyle 14?

Options

A6/35\displaystyle 6/35
B8/35\displaystyle 8/35
C10/35\displaystyle 10/35
DNone of these
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Correct Answer

✅ Option d — None of these

All Options:

  • A6/35\displaystyle 6/35
  • B8/35\displaystyle 8/35
  • C10/35\displaystyle 10/35
  • DNone of these

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Detailed Solution & Explanation

**Probability of Selecting a Multiple of 5 or 14** Total natural numbers = 70 (from 1 to 70) Let A\displaystyle A be the event of selecting a multiple of 5. n(A)=⌊705⌋=14n(A) = \lfloor \frac{70}{5} \rfloor = 14 Let B\displaystyle B be the event of selecting a multiple of 14. n(B)=⌊7014⌋=5n(B) = \lfloor \frac{70}{14} \rfloor = 5 Let A∩B\displaystyle A \cap B be the event of selecting a multiple of both 5 and 14 (i.e., a multiple of 70). In this range, the only multiple is 70. n(A∩B)=1n(A \cap B) = 1 By the Addition Theorem of Probability: n(A∪B)=n(A)+n(B)−n(A∩B)=14+5−1=18n(A \cup B) = n(A) + n(B) - n(A \cap B) = 14 + 5 - 1 = 18 Thus, the probability is: P(A∪B)=1870=935P(A \cup B) = \frac{18}{70} = \frac{9}{35} Since 935\displaystyle \frac{9}{35} is not listed in Options A, B, or C, the correct choice is None of these. 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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