ProbabilityMCQMTP May 19 Series IIQuestion 2813 of 295
All Questions

What is the chance of throwing at least 7 in a single cast with 2 dice?

Options

A512\displaystyle \frac{5}{12}
B712\displaystyle \frac{7}{12}
C14\displaystyle \frac{1}{4}
D1763\displaystyle \frac{17}{63}
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Correct Answer

✅ Option b — 712\displaystyle \frac{7}{12}

All Options:

  • A512\displaystyle \frac{5}{12}
  • B712\displaystyle \frac{7}{12}
  • C14\displaystyle \frac{1}{4}
  • D1763\displaystyle \frac{17}{63}

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Detailed Solution & Explanation

When two dice are cast: 1. **Total number of outcomes** is: 6×6=366 \times 6 = 36 2. Let X\displaystyle X be the sum of numbers on the two dice. We want to find the probability of throwing "at least 7", which means X≥7\displaystyle X \ge 7. 3. Let's count the number of favorable outcomes for each sum from 7 to 12: - **Sum = 7:** (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)  ⟹  6\displaystyle (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) \implies 6 outcomes - **Sum = 8:** (2,6),(3,5),(4,4),(5,3),(6,2)  ⟹  5\displaystyle (2,6), (3,5), (4,4), (5,3), (6,2) \implies 5 outcomes - **Sum = 9:** (3,6),(4,5),(5,4),(6,3)  ⟹  4\displaystyle (3,6), (4,5), (5,4), (6,3) \implies 4 outcomes - **Sum = 10:** (4,6),(5,5),(6,4)  ⟹  3\displaystyle (4,6), (5,5), (6,4) \implies 3 outcomes - **Sum = 11:** (5,6),(6,5)  ⟹  2\displaystyle (5,6), (6,5) \implies 2 outcomes - **Sum = 12:** (6,6)  ⟹  1\displaystyle (6,6) \implies 1 outcome 4. **Total number of favorable outcomes** is: 6+5+4+3+2+1=216 + 5 + 4 + 3 + 2 + 1 = 21 5. The probability of throwing at least 7 is: Probability=2136=712\text{Probability} = \frac{21}{36} = \frac{7}{12} 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.

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