ProbabilityMCQMTP Nov 21Question 2804 of 295
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The probability that a leap year has 53 Wednesday is:

Options

A27\displaystyle \frac{2}{7}
B53\displaystyle \frac{5}{3}
C23\displaystyle \frac{2}{3}
D17\displaystyle \frac{1}{7}
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Correct Answer

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

All Options:

  • A27\displaystyle \frac{2}{7}
  • B53\displaystyle \frac{5}{3}
  • C23\displaystyle \frac{2}{3}
  • D17\displaystyle \frac{1}{7}

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Detailed Solution & Explanation

To find the probability of a leap year having 53 Wednesdays: 1. A leap year has **366 days**. 2. A week has 7 days. Calculating the number of weeks: 366 days=52 weeks×7 days/week+2 extra days=364 days+2 extra days366 \text{ days} = 52 \text{ weeks} \times 7 \text{ days/week} + 2 \text{ extra days} = 364 \text{ days} + 2 \text{ extra days} 3. Therefore, a leap year contains 52 complete weeks (which guarantees at least 52 Wednesdays) and **2 extra consecutive days**. 4. The possible combinations for these 2 extra days can be any of the following 7 equally likely pairs: - (Monday, Tuesday) - (Tuesday, Wednesday) - (Wednesday, Thursday) - (Thursday, Friday) - (Friday, Saturday) - (Saturday, Sunday) - (Sunday, Monday) 5. Out of these 7 possible combinations, Wednesdays occur in exactly 2 cases: - (Tuesday, Wednesday) - (Wednesday, Thursday) 6. Thus, the number of favorable cases is 2, and the total number of possible cases is 7. Probability=27\text{Probability} = \frac{2}{7} 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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