The question involves knowing leap year and number of days in a year..

So, let us talk of this question in two different cases..
(1) A normal year
It has 365 days which is 52 weeks and 1 day. So any of the 7 days from Sunday to Saturday that the year starts with will be 53 and rest 6 will be 52. Probability of Sunday will be as any of other seven so \(\frac{1}{7}\).
(2) A Leap year
It has 366 days which is 52 weeks and 2 days. So any 2 of the 7 days from Sunday to Saturday that the year starts with will be 53 and rest 5 will be 52. Probability of Sunday will be as any of other seven so \(2*\frac{1}{7}=\frac{2}{7}\). Multiplication by 2 is because we have 2 days that can be 53.

Now we have to check the probability of a normal year and a leap year.
Here, we will take a standard case that every 4th year is leap year and will not consider the 1000th year as non-leap
so Probability of normal year is 3/4 and that of leap year is 1/4.

Answer \(\frac{3}{4}*\frac{1}{7}+\frac{1}{4}*\frac{2}{7}=\frac{5}{28}\)

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Non leap year case: (365 % 7) = 1, (every day in a week, repeats 52 times), now for 53 sundays, the remaining last day has to be sunday, then Jan 1 of that year must be sunday.

probability of 53 sundays = (3/4)(probability of non-leap year) * (1/7) ( probability of jan1 of that year to be sunday) = 3/28

Leap year case: (366 % 7) = 2, (every day in a week, repeats 52 times), now two days remaining, for 53 sundays, either of last two days must be sunday, then Jan 1 of that year has to be either saturday or sunday.

probability of 53 sundays = (1/4) (probability of leap year) * (2/7) (probability of jan 1 of that year to be either sunday or saturday) = 2/28

so total probability (leap year case + non leap year case) = (3/28) + (2/28) = 5/28