**Probability of 53 Sundays in a Leap Year**

To calculate the probability of having 53 Sundays in a leap year, we need to understand some key concepts and calculations related to leap years and the days of the week.

**Leap Year:**
A leap year is a year that contains an additional day, February 29th, making it 366 days long instead of the usual 365 days. Leap years are necessary to keep our calendar in alignment with the Earth's revolutions around the Sun.

**Days of the Week:**
In a non-leap year, there are 365 days, which is equivalent to 52 weeks and 1 day. This means that each day of the week occurs 52 times, except for one day which occurs 53 times. In a leap year, with 366 days, each day of the week occurs 52 times, and there are two days that occur 53 times.

**Calculating the Probability:**

1. Calculate the total number of possible outcomes:
In a leap year, there are a total of 366 days. Therefore, the total number of possible outcomes is 366.

2. Identify the favorable outcomes:
To have 53 Sundays in a leap year, we need to determine the number of occurrences of Sunday within that year. As mentioned earlier, in a leap year, there are two days that occur 53 times. So, the favorable outcomes are 2.

3. Calculate the probability:
Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes.
Probability = Favorable Outcomes / Possible Outcomes

In this case, the probability of having 53 Sundays in a leap year is:
Probability = 2 / 366

4. Simplify the fraction:
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2 in this case.
Probability = 1 / 183

Therefore, the probability of having 53 Sundays in a leap year is 1/183.

It is important to note that this probability assumes that each day of the week is equally likely to occur on any given year. However, in reality, the distribution of days can vary due to various factors such as the starting day of the year and the occurrence of leap years.

The possible pairs are( Saturday,Sunday) (Sunday, Monday). so n(E) =2. therefore the probability of a leap year having 53 sundays=n(E)/n(S)=2/7
I hope it may help you