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    What is the Probability of 52 Sundays in a Leap Year?

    Probability Calculator

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

    P(A) = 5/7 = 0.71

    How to find probability of 52 Sundays in a leap year?

    Users may refer the below detailed information to learn how to find the probability of 52 Sundays 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 {Saturday & Sunday} or {Sunday & Monday} is enough to find the probability of getting 52 Sundays 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 = {Mon & Tue}, {Tue & Wed}, {Wed & Thu}, {Thu & Fri}, {Fri & Sat}
    P(A) = {Mon & Tue}, {Tue & Wed}, {Wed & Thu}, {Thu & Fri}, {Fri & Sat}/{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 {Saturday & Sunday} or {Sunday & Monday}
    The sample space S = {Sunday & Monday, Monday & Tuesday, Tuesday & Wednesday, Wednesday & Thursday, Thursday & Friday, Friday & Saturday, Saturday & Sunday}
    Expected events of A = {Saturday & Sunday}, {Sunday & Monday}

    P(A)={Saturday & Sunday}, {Sunday & Monday}/{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 {Saturday & Sunday}, {Sunday & Monday}
    = 1 - P(A)
    = 1 - 0.29
    P(A’) = 0.71

    0.71 is probability for 52 Sundays in a leap year.

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