ProbabilityMCQMTP Dec 22 Series IIQuestion 3298 of 187
All Questions

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}
C815\displaystyle \frac{8}{15}
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}
  • C815\displaystyle \frac{8}{15}
  • D17\displaystyle \frac{1}{7}

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Detailed Solution & Explanation

**Two Dice — At Least One 5 (Repeated)** Total outcomes = 6×6=36\displaystyle 6 \times 6 = 36 Using complement: 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}) =1−56×56=1−2536=1136= 1 - \frac{5}{6} \times \frac{5}{6} = 1 - \frac{25}{36} = \frac{11}{36} **Direct enumeration:** Outcomes with at least one 5: - Die 1 = 5: 6 outcomes - Die 2 = 5 (Die 1 ≠ 5): 5 outcomes - Total = 11 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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