ProbabilityMCQMTP June 2023 Series IQuestion 3301 of 187
All Questions

The probability that a leap year has 53\displaystyle 53 Sunday is:

Options

A17\displaystyle \frac{1}{7}
B27\displaystyle \frac{2}{7}
C27\displaystyle \frac{2}{7}
D35\displaystyle \frac{3}{5}
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Correct Answer

✅ Option b — 27\displaystyle \frac{2}{7}

All Options:

  • A17\displaystyle \frac{1}{7}
  • B27\displaystyle \frac{2}{7}
  • C27\displaystyle \frac{2}{7}
  • D35\displaystyle \frac{3}{5}

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Detailed Solution & Explanation

**Probability of 53 Sundays in a Leap Year** A leap year has 366 days = 52 weeks + 2 extra days. The 7 possible pairs of extra consecutive days: (Sun,Mon), (Mon,Tue), (Tue,Wed), (Wed,Thu), (Thu,Fri), (Fri,Sat), (Sat,Sun)(Sun,Mon),\ (Mon,Tue),\ (Tue,Wed),\ (Wed,Thu),\ (Thu,Fri),\ (Fri,Sat),\ (Sat,Sun) Pairs containing Sunday: - (Sun,Mon)\displaystyle (Sun, Mon) → has Sunday - (Sat,Sun)\displaystyle (Sat, Sun) → has Sunday Favorable = **2**, Total = **7** P(53 Sundays in a leap year)=27P(53 \text{ Sundays in a leap year}) = \frac{2}{7} Note: The given correct_option "a" = 17\displaystyle \frac{1}{7} applies to a **non-leap year** (365 days = 52 weeks + 1 extra day). For a leap year, the answer is 27\displaystyle \frac{2}{7} = Options B or C. By mathematical derivation for a **leap year**: P=27P = \frac{2}{7} 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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