What is the probability of getting 53 Fridays in a leap year?
Introduction:
Getting 53 Fridays in a leap year is an interesting mathematical problem. It requires understanding the concept of leap year and the number of days in a year. In this response, we will discuss the probability of getting 53 Fridays in a leap year and explain the concept in detail.
Leap Year:
A leap year is a year that has 366 days instead of the usual 365 days. It occurs every four years and is necessary to keep the calendar year synchronized with the astronomical or seasonal year.
Number of Fridays in a Year:
There are 52 weeks in a year, and since there are seven days in a week, there are a total of 364 days in a year. Therefore, there are 52 Fridays in a regular year.
Probability of Getting 53 Fridays in a Leap Year:
To get 53 Fridays in a leap year, we need an additional Friday, which means that there must be 53 weeks in that year. This can happen only if the 1st of January falls on a Friday.
Calculation:
The probability of the 1st of January falling on a Friday is 1/7. Therefore, the probability of getting 53 Fridays in a leap year is:
1/7 x 1 = 1/7
Conclusion:
In conclusion, the probability of getting 53 Fridays in a leap year is 1/7, which means that it is a rare occurrence. It happens only when the 1st of January falls on a Friday. The concept of leap year and the number of days in a year are essential to understanding this problem.
What is the probability of getting 53 Fridays in a leap year?
A leap year consists of 366 days, i.e., 52 complete weeks and 2 days remain. These 2 days can be any of the following:
(Mon, Tues), (Tues, Wed), (Wed, Thur), (Thur, Fri), (Fri, Sat), (Sat, Sun)
Thus, total number of cases = 7
Number of cases in which we get a Friday = 2
∴Probability of getting 53 Fridays in a leap year = 2/7