ProbabilityMCQMTP March 21Question 2800 of 295
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In a non-leap year, the probability of getting 53 Sundays or 53 Tuesday or 53 Thursday is:

Options

A47\displaystyle \frac{4}{7}
B27\displaystyle \frac{2}{7}
C37\displaystyle \frac{3}{7}
D17\displaystyle \frac{1}{7}
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Correct Answer

✅ Option c — 37\displaystyle \frac{3}{7}

All Options:

  • A47\displaystyle \frac{4}{7}
  • B27\displaystyle \frac{2}{7}
  • C37\displaystyle \frac{3}{7}
  • D17\displaystyle \frac{1}{7}

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Detailed Solution & Explanation

A non-leap year has 365 days, which is equivalent to 52 weeks and 1 extra day. - The 52 weeks guarantee exactly 52 of each weekday. - The occurrence of a 53rd day depends entirely on the remaining 1 day. - The remaining 1 day has 7 equally likely possibilities: {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}. We want the probability of getting 53 Sundays, 53 Tuesdays, or 53 Thursdays. Since only one of these days can be the 53rd day (the events are mutually exclusive), the favorable outcomes for the extra day are {Sunday, Tuesday, Thursday}. There are 3 favorable outcomes out of 7 possible outcomes. Thus, the probability is: Probability=37\text{Probability} = \frac{3}{7} This corresponds to Option C. 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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