ProbabilityMCQMTP June 2023 Series IIQuestion 3303 of 187
All Questions

If two dice are thrown then what is the probability that the sum of the faces of dice are square or cube number?

Options

A14\displaystyle \frac{1}{4}
B12\displaystyle \frac{1}{2}
C13\displaystyle \frac{1}{3}
DNone of these
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Correct Answer

✅ Option c — 13\displaystyle \frac{1}{3}

All Options:

  • A14\displaystyle \frac{1}{4}
  • B12\displaystyle \frac{1}{2}
  • C13\displaystyle \frac{1}{3}
  • DNone of these

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Detailed Solution & Explanation

**Sum is Perfect Square or Perfect Cube (Two Dice)** Total outcomes = 36. Possible sums range from 2 to 12. **Perfect squares** in range [2,12]: 4,9\displaystyle 4, 9 (since 4=22\displaystyle 4=2^2, 9=32\displaystyle 9=3^2; 16>12\displaystyle 16 > 12) **Perfect cubes** in range [2,12]: 8\displaystyle 8 (since 8=23\displaystyle 8=2^3; 27>12\displaystyle 27 > 12) **Combined (squares or cubes):** {4,8,9}\displaystyle \{4, 8, 9\} Favorable outcomes: **Sum = 4:** (1,3),(2,2),(3,1)\displaystyle (1,3),(2,2),(3,1) → 3 outcomes **Sum = 8:** (2,6),(3,5),(4,4),(5,3),(6,2)\displaystyle (2,6),(3,5),(4,4),(5,3),(6,2) → 5 outcomes **Sum = 9:** (3,6),(4,5),(5,4),(6,3)\displaystyle (3,6),(4,5),(5,4),(6,3) → 4 outcomes **Total favorable** = 3+5+4=12\displaystyle 3 + 5 + 4 = 12 P=1236=13P = \frac{12}{36} = \frac{1}{3} Hence, **Option C** 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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