ProbabilityMCQMTP Jun 24 Series IQuestion 3364 of 187
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Three identical dice are rolled. The probability that the same number will appear on each of them is:

Options

A1/6\displaystyle 1/6
B1/12\displaystyle 1/12
C1/36\displaystyle 1/36
D1\displaystyle 1
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Correct Answer

✅ Option c — 1/36\displaystyle 1/36

All Options:

  • A1/6\displaystyle 1/6
  • B1/12\displaystyle 1/12
  • C1/36\displaystyle 1/36
  • D1\displaystyle 1

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Detailed Solution & Explanation

**Probability of the Same Number on Three Dice** When three identical dice are rolled simultaneously: **Step 1: Total possible outcomes** Each die has 6 faces, so for three dice, the total number of outcomes is: Total outcomes=63=216\text{Total outcomes} = 6^3 = 216 **Step 2: Favorable outcomes** The event that the same number appears on all three dice consists of the following outcomes: {(1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6)}\{(1,1,1), (2,2,2), (3,3,3), (4,4,4), (5,5,5), (6,6,6)\} There are exactly 6 favorable outcomes. **Step 3: Probability calculation** P=Favorable outcomesTotal outcomes=6216=136P = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{6}{216} = \frac{1}{36} 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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