ProbabilityMCQPYQ Nov. 18Question 3273 of 187
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Two different dice are thrown simultaneously, then the probability that the sum of two numbers appearing on the top of dice is 9\displaystyle 9 is:

Options

A89\displaystyle \frac{8}{9}
B19\displaystyle \frac{1}{9}
C79\displaystyle \frac{7}{9}
DNone of these
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Correct Answer

✅ Option b — 19\displaystyle \frac{1}{9}

All Options:

  • A89\displaystyle \frac{8}{9}
  • B19\displaystyle \frac{1}{9}
  • C79\displaystyle \frac{7}{9}
  • DNone of these

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Detailed Solution & Explanation

**Probability that Sum of Two Dice = 9** Total outcomes when two dice are thrown = 6×6=36\displaystyle 6 \times 6 = 36 Favorable outcomes where sum = 9: - (3,6)\displaystyle (3, 6): 3+6=9\displaystyle 3 + 6 = 9 ✓ - (4,5)\displaystyle (4, 5): 4+5=9\displaystyle 4 + 5 = 9 ✓ - (5,4)\displaystyle (5, 4): 5+4=9\displaystyle 5 + 4 = 9 ✓ - (6,3)\displaystyle (6, 3): 6+3=9\displaystyle 6 + 3 = 9 ✓ Number of favorable outcomes = **4** P(sum=9)=436=19P(\text{sum} = 9) = \frac{4}{36} = \frac{1}{9} 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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