ProbabilityMCQPYQ Dec 22Question 3286 of 187
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The probability that a leap year has 53\displaystyle 53 Monday is:

Options

A17\displaystyle \frac{1}{7}
B23\displaystyle \frac{2}{3}
C27\displaystyle \frac{2}{7}
D35\displaystyle \frac{3}{5}
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Correct Answer

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

All Options:

  • A17\displaystyle \frac{1}{7}
  • B23\displaystyle \frac{2}{3}
  • C27\displaystyle \frac{2}{7}
  • D35\displaystyle \frac{3}{5}

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Detailed Solution & Explanation

**Probability of 53 Mondays in a Leap Year** A leap year has **366 days** = 52\displaystyle 52 complete weeks + **2 extra days**. The 52 complete weeks already contain 52 Mondays. For a 53rd Monday, one of the 2 extra days must be a Monday. The 7 equally likely consecutive day-pairs for the 2 extra 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)\} Total pairs = **7** Pairs containing Monday: - (Sun,Mon)\displaystyle (Sun, Mon) - (Mon,Tue)\displaystyle (Mon, Tue) Favorable = **2** P(53 Mondays in leap year)=27P(53 \text{ Mondays in leap year}) = \frac{2}{7} Hence, **Option C** 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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