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

getcalc.com's Probability calculator to find what is the probability of 52 Mondays 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 {Sunday & Monday} or {Monday & Tuesday} is the probability of getting 52 Mondays for a leap year.

P(A) = 5/7 = 0.71

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

Users may refer the below detailed information to learn how to find the probability of 52 Mondays 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 {Sunday & Monday} or {Monday & Tuesday} is enough to find the probability of getting 52 Mondays 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 = {Tue & Wed}, {Wed & Thu}, {Thu & Fri}, {Fri & Sat}, {Sat & Sun}

P(A) = {Tue & Wed}, {Wed & Thu}, {Thu & Fri}, {Fri & Sat}, {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 {Sunday & Monday} or {Monday & Tuesday}

The sample space S = {Sunday & Monday, Monday & Tuesday, Tuesday & Wednesday, Wednesday & Thursday, Thursday & Friday, Friday & Saturday, Saturday & Sunday}

Expected events of A = {Sunday & Monday}, {Monday & Tuesday}

P(A)={Sunday & Monday}, {Monday & Tuesday}/{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 {Sunday & Monday}, {Monday & Tuesday}

= 1 - P(A)

= 1 - 0.29

P(A’) = 0.71

0.71 is probability for 52 Mondays in a leap year.