ProbabilityMCQPYQ May 18Question 3319 of 187
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What is the probability of having at least one '6\displaystyle 6' in 3\displaystyle 3 throws of a project die?

Options

A56\displaystyle \frac{5}{6}
B1−(56)3\displaystyle 1-(\frac{5}{6})^3
C1−(16)3\displaystyle 1-(\frac{1}{6})^3
D163\displaystyle \frac{1}{6^3}
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Correct Answer

✅ Option b — 1−(56)3\displaystyle 1-(\frac{5}{6})^3

All Options:

  • A56\displaystyle \frac{5}{6}
  • B1−(56)3\displaystyle 1-(\frac{5}{6})^3
  • C1−(16)3\displaystyle 1-(\frac{1}{6})^3
  • D163\displaystyle \frac{1}{6^3}

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Detailed Solution & Explanation

**At Least One 6 in 3 Throws of a Die** Using the complement rule: P(at least one 6)=1−P(no 6 in any of 3 throws)P(\text{at least one 6}) = 1 - P(\text{no 6 in any of 3 throws}) P(no 6 in one throw)=56\displaystyle P(\text{no 6 in one throw}) = \frac{5}{6} Since throws are independent: P(no 6 in all 3 throws)=(56)3P(\text{no 6 in all 3 throws}) = \left(\frac{5}{6}\right)^3 P(at least one 6)=1−(56)3P(\text{at least one 6}) = 1 - \left(\frac{5}{6}\right)^3 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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