ProbabilityMCQPYQ Dec 23Question 3337 of 187

A number is selected from the first $\displaystyle 30$ natural numbers. What is the probability that it would be divisible by $\displaystyle 3$ or $\displaystyle 8$ ?

Options

\displaystyle 0.2

\displaystyle 0.4

\displaystyle 0.6

\displaystyle 0.8

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Correct Answer

✅ Option b — $\displaystyle 0.4$

All Options:

A $\displaystyle 0.2$
B $\displaystyle 0.4$
C $\displaystyle 0.6$
D $\displaystyle 0.8$

Detailed Solution & Explanation

**Probability of Selecting a Number Divisible by 3 or 8** The total number of outcomes is

\displaystyle 30

(numbers from 1 to 30). Let

\displaystyle A

be the event that the number is divisible by 3. The multiples of 3 in this range are:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30

So,

\displaystyle n(A) = 10

. Let

\displaystyle B

be the event that the number is divisible by 8. The multiples of 8 in this range are:

8, 16, 24

So,

\displaystyle n(B) = 3

. The event

\displaystyle A \cap B

is when the number is divisible by both 3 and 8 (i.e., divisible by 24). In the range 1 to 30, the only such number is 24. So,

\displaystyle n(A \cap B) = 1

. By the Addition Theorem of Probability:

n(A \cup B) = n(A) + n(B) - n(A \cap B) = 10 + 3 - 1 = 12

Thus, the probability of selecting a number divisible by 3 or 8 is:

P(A \cup B) = \frac{12}{30} = 0.4

This matches Option B. (Note: The official answer key incorrectly lists Option D as correct, but mathematically it is 0.4). 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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A number is selected from the first 30\displaystyle 3030 natural numbers. What is the probability that it would be divisible by 3\displaystyle 33 or 8\displaystyle 88?