# What is the Probability of 52 Fridays in a Leap Year?

getcalc.com's Probability calculator to find what is the probability of 52 Fridays in a leap year. The ratio of expected event to all the possible events of a sample space for 2 odd days not to be {Thursday & Friday} or {Friday & Saturday} is the probability of getting 52 Fridays for a leap year.

P(A) = 5/7 = 0.71

## How to find probability of 52 Fridays in a leap year?

Users may refer the below detailed information to learn how to find the probability of 52 Fridays in a leap year. The total number of weeks in a leap year {366 days = 52 (2/7)} is 52 weeks and two odd days. Since, finding the probability for the two odd days not to be either {Thursday & Friday} or {Friday & Saturday} is enough to find the probability of getting 52 Fridays in a leap year of a Gregorian calendar by using any one of the following two methods.
Direct Method :
Workout
step 1 Possible outcomes for 2 odd days
The 2 odd days may be the combination of Sunday & Monday, Monday & Tuesday, Tuesday & Wednesday, Wednesday & Thursday, Thursday & Friday, Friday & Saturday or Saturday & Sunday. Therefore, the total number of possible outcomes or elements of a sample space is 7.

step 2 Probability of 2 Odd days not to be Monday & Tuesday, Tuesday & Wednesday, Wednesday & Thursday, Thursday & Friday or Friday & Saturday
The sample space S = {Sunday & Monday, Monday & Tuesday, Tuesday & Wednesday, Wednesday & Thursday, Thursday & Friday, Friday & Saturday, Saturday & Sunday}
Expected events of A = {Sun & Mon}, {Mon & Tue}, {Tue & Wed}, {Wed & Thu}, {Sat & Sun}
P(A) = {Sun & Mon}, {Mon & Tue}, {Tue & Wed}, {Wed & Thu}, {Sat & Sun}/{Sun & Mon}, . . . , {Sat & Sun}
P(A) = A/S = 5/7
P(A) = 0.71

5/7 or 0.71 is probability for 52 Sundays in a leap year.

Complement Method :
Workout
step 1 Possible outcomes for 2 odd days
The two odd days may be the combination of Sunday & Monday, Monday & Tuesday, Tuesday & Wednesday, Wednesday & Thursday, Thursday & Friday, Friday & Saturday or Saturday & Sunday. Therefore, the total number of possible outcomes or elements of a sample space is 7.

step 2 Probability of 2 Odd days to be {Thursday & Friday} or {Friday & Saturday}
The sample space S = {Sunday & Monday, Monday & Tuesday, Tuesday & Wednesday, Wednesday & Thursday, Thursday & Friday, Friday & Saturday, Saturday & Sunday}
Expected events of A = {Thursday & Friday}, {Friday & Saturday}

P(A)={Thursday & Friday}, {Friday & Saturday}/{Sunday & Monday}, . . . , {Saturday & Sunday}
P(A) = A/S = 2/7
P(A) = 0.29

step 3 Finding the complement of events A to have two odd days not to be {Thursday & Friday}, {Friday & Saturday}
= 1 - P(A)
= 1 - 0.29
P(A’) = 0.71

0.71 is probability for 52 Fridays in a leap year.