ProbabilityMCQPYQ June 19Question 3265 of 187
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When 2\displaystyle 2 - dice are thrown simultaneously then the probability of getting at least one 5\displaystyle 5 is

Options

A1136\displaystyle \frac{11}{36}
B536\displaystyle \frac{5}{36}
C118\displaystyle \frac{1}{18}
D17\displaystyle \frac{1}{7}
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Correct Answer

✅ Option a — 1136\displaystyle \frac{11}{36}

All Options:

  • A1136\displaystyle \frac{11}{36}
  • B536\displaystyle \frac{5}{36}
  • C118\displaystyle \frac{1}{18}
  • D17\displaystyle \frac{1}{7}

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Detailed Solution & Explanation

**Two Dice Thrown — At Least One 5** Total outcomes when 2 dice are thrown = 6×6=36\displaystyle 6 \times 6 = 36 Using the complement rule: P(at least one 5)=1−P(no 5 on either die)P(\text{at least one 5}) = 1 - P(\text{no 5 on either die}) P(no 5 on one die)=56\displaystyle P(\text{no 5 on one die}) = \frac{5}{6} P(no 5 on either die)=56×56=2536\displaystyle P(\text{no 5 on either die}) = \frac{5}{6} \times \frac{5}{6} = \frac{25}{36} Therefore: P(at least one 5)=1−2536=1136P(\text{at least one 5}) = 1 - \frac{25}{36} = \frac{11}{36} **Verification by direct count:** Outcomes with at least one 5: - First die = 5: (5,1),(5,2),(5,3),(5,4),(5,5),(5,6) → 6 outcomes - Second die = 5: (1,5),(2,5),(3,5),(4,5),(6,5) → 5 outcomes (excluding (5,5) already counted) - Total = 11 outcomes P=1136P = \frac{11}{36} Hence, **Option A** 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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