ProbabilityMCQPYQ Nov. 20Question 3323 of 187
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When 2\displaystyle 2 fair dice are thrown, what is the probability of getting the sum which is a multiple of 3\displaystyle 3?

Options

A436\displaystyle \frac{4}{36}
B1336\displaystyle \frac{13}{36}
C236\displaystyle \frac{2}{36}
D1236\displaystyle \frac{12}{36}
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Correct Answer

✅ Option d — 1236\displaystyle \frac{12}{36}

All Options:

  • A436\displaystyle \frac{4}{36}
  • B1336\displaystyle \frac{13}{36}
  • C236\displaystyle \frac{2}{36}
  • D1236\displaystyle \frac{12}{36}

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Detailed Solution & Explanation

**Sum is Multiple of 3 (Two Dice)** Total outcomes = 36 Multiples of 3 in range [2,12]: 3,6,9,12\displaystyle 3, 6, 9, 12 **Sum = 3:** (1,2),(2,1)\displaystyle (1,2),(2,1) → 2 outcomes **Sum = 6:** (1,5),(2,4),(3,3),(4,2),(5,1)\displaystyle (1,5),(2,4),(3,3),(4,2),(5,1) → 5 outcomes **Sum = 9:** (3,6),(4,5),(5,4),(6,3)\displaystyle (3,6),(4,5),(5,4),(6,3) → 4 outcomes **Sum = 12:** (6,6)\displaystyle (6,6) → 1 outcome Total favorable = 2+5+4+1=12\displaystyle 2 + 5 + 4 + 1 = 12 P(sum is multiple of 3)=1236=13P(\text{sum is multiple of 3}) = \frac{12}{36} = \frac{1}{3} 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.

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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