Question:
A year selected at random has 365 days. The probability that it has 53 Sundays is:
A year selected at random has 365 days. The probability that it has 53 Sundays is:
Show Hint
Calendar probability depends on starting day.
Updated On: Jan 4, 2026
- \(\frac{1}{7}\)
- \(\frac{2}{7}\)
- \(\frac{1}{365}\)
\(\frac{53}{365}\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
To determine the probability that a random year has 53 Sundays, let's analyze the situation:
- Understanding the Structure of a Year: A typical year has 365 days. These 365 days can be divided into 52 weeks and 1 extra day (since 365 ÷ 7 = 52 weeks and 1 day).
- Identifying the Day of the Extra Day: Since there is 1 day left after dividing the year into weeks, the day of the week that this extra day represents determines whether there will be 53 occurrences of that day in the year. For instance, if the year starts on a Sunday, then Sunday is the extra day.
- Calculating the Probability: In a non-leap year of 365 days, every day of the week (Sunday, Monday, …, Saturday) has an equal probability of being the extra day. There are 7 possible choices for the extra day.
- Probability of 53 Sundays: If the extra day is Sunday, then there will be 53 Sundays in that year. Therefore, the probability of having 53 Sundays is the fraction of favorable outcomes over the total number of outcomes, which is:
\(\frac{1}{7}\) because there is 1 favorable outcome (having Sunday as the extra day) out of 7 possible outcomes (any day of the week can be an extra day).
Thus, the correct answer is:
\(\frac{1}{7}\).
Was this answer helpful?
0
0
Top XAT General Aptitude Questions
- While no one made any _________ the financial scandal while he was in the room, there was a feeling of awe to the _________ created by the broker that had snared many unsuspecting investors under the _________ that everyone would end up rich and the fact that he had been celebrating his _________ of the legal authorities by attending parties. The option that best fills the blanks in the above paragraph would be:
- “So you want me to proscribe Ceecee…” The most suitable inference about Ceecee can be:
- The boss called to inform that he _________ be coming to office that day. However the employees did not take it easy as they knew it was his _________ to give them a surprise by coming in and checking who was at work. Any employee, once caught not working, would then be required to _________ on the reasons for not working and if the boss was not satisfied the employee had to work on Sunday to _________ the wrong. The option that best fills the blanks in the above paragraph would be:
- “In the election of 2009, the internet emerged as the new communication _________ to be used by political parties to inform the voters about their agenda.” The option that best fills the blank would be:
- _________ children in rains run the risk of getting lost. The option that best fills the blank would be:
View More Questions
Top XAT Quantitative Aptitude Questions
- In a circular field, AOB and COD are two mutually perpendicular diameters having length of 4 meters. X is the mid-point of OA. Y is the point on the circumference such that $\angle YOD = 30^\circ$. Which of the following correctly gives the relation among the three alternate paths from X to Y?
- If x and y are real numbers, then the minimum value of $x^2 + 4xy + 6y^2 - 4y + 4$ is
- Let X be a four-digit positive integer such that the unit digit of X is prime and the product of all 4 digits of X is also prime. How many such integers are possible?
- There are two types of employees in Sun Metals, general graduates and engineers. 40% of the employees in Sun Metals are general graduates, and 75% of the engineers earn more than Rs. 5 lakh/year. If 50% of the organisation’s employees earn more than Rs. 5 lakh/year, what proportion of the general graduates employed by the organisation earn Rs. 5 lakh or less?
- In an equilateral triangle ABC, whose length of each side is 3 cm, D is the point on BC such that BD = (1/2) CD. What is the length of AD?
View More Questions
Top XAT Questions
- Ashok, a maths teacher in the school, asked his students to guess his date of birth by giving the following hints.
Hint 1: He was born in 1995
Hint 2: The sum of the products of his birth date multiplied by 24 and his birthday month multiplied by 60 is 1284.
Find the sum of Ashok’s birth date, birth month, and birth year. - Solve for the number of integral values of \(x: \frac{(x^2-15x+47)(x-13)}{(x-8)}<0\).
- In an examination, Akhil scored 11.11% less than the pass marks and Akshay scored 12.5% more than the pass marks. Find the percentage of pass marks if the sum of the scores of Akhil and Akshay is 25% more than the total marks.
- The ratio of paint and oil in Tank A is 3: 4, whereas in Tank B, the respective ratio is 4: 5 . Then, 96 liters of a mixture consisting of paint and oil in the ratio of 5: 1 is added to Tank A, such that the respective ratio in Tank A becomes exactly the reverse of that in Tank B. Find the amount (in liters) of the mixture from Tank B that is poured into Tank A such that the amount of paint and water in Tank A become equal.
- The points (–4, 3) and (–1, –4) are two end points of a diagonal of a parallelogram. If the other diagonal has the equation 7y + 3x + c = 0, then find the value of c.
View More Questions