ProbabilityMCQPYQ June 22Question 3283 of 187
All Questions

What is the probability of occurrence of leap year having 53\displaystyle 53 Sunday?

Options

A17\displaystyle \frac{1}{7}
B27\displaystyle \frac{2}{7}
C37\displaystyle \frac{3}{7}
D47\displaystyle \frac{4}{7}
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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}
  • C37\displaystyle \frac{3}{7}
  • D47\displaystyle \frac{4}{7}

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Detailed Solution & Explanation

**Probability of 53 Sundays in a Leap Year** A leap year has **366 days** = 52\displaystyle 52 complete weeks + **2 extra days**. The 52 complete weeks already have 52 Sundays. For a 53rd Sunday, one of the 2 extra days must be a Sunday. The 2 extra days are consecutive, and the 7 equally likely pairs are: {(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 that include Sunday: - (Sun,Mon)\displaystyle (Sun, Mon) - (Sat,Sun)\displaystyle (Sat, Sun) Favorable outcomes = **2** P(53 Sundays in a leap year)=27P(53 \text{ Sundays in a leap year}) = \frac{2}{7} This equals **Option B** = 27\displaystyle \frac{2}{7}. The given correct_option is "a" = 17\displaystyle \frac{1}{7}, which is the probability for a non-leap year (365 days = 52 weeks + 1 extra day; 1 out of 7 days can be Sunday). By mathematical derivation for a **leap year**: P=27\displaystyle P = \frac{2}{7} = Option B. 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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