Probability of a Leap Year Containing 53 Days

A leap year is a year that contains an extra day, February 29th, which is added to keep the calendar year synchronized with the solar year. The probability of a leap year containing 53 days can be determined by considering the rules and patterns of leap years.

Understanding Leap Years:
- A regular year has 365 days, while a leap year has 366 days.
- Leap years occur every 4 years, except for years that are divisible by 100 but not divisible by 400.
- This means that the year 2000 was a leap year, as it is divisible by 400, but the year 1900 was not a leap year, as it is divisible by 100 but not divisible by 400.

Determining the Probability:
To determine the probability of a randomly selected leap year containing 53 days, we need to consider the total number of leap years and the number of those leap years that contain 53 days.

Total Number of Leap Years:
- Leap years occur every 4 years, so the total number of leap years within a given range can be calculated by dividing the number of years in that range by 4.
- For example, if we consider a 100-year range, we would have 100/4 = 25 leap years.

Number of Leap Years with 53 Days:
- To determine the number of leap years that contain 53 days, we need to identify the years in which February 29th falls on a Sunday.
- This occurs every 28 years because there are 7 possible days of the week for February 29th to fall on (Sunday, Monday, Tuesday, etc.).
- Therefore, within a 100-year range, there would be 100/28 = 3.57, which we can round down to 3 leap years with 53 days.

Calculating the Probability:
To calculate the probability, we divide the number of leap years with 53 days by the total number of leap years.

Probability = Number of Leap Years with 53 Days / Total Number of Leap Years

In this case:
- Number of Leap Years with 53 Days = 3
- Total Number of Leap Years = 25

Probability = 3 / 25 = 0.12 or 12%

Therefore, the probability that a leap year selected at random would contain 53 days is 12%.